Lesson 4.2 Understanding Slope-intercept Form

Learning Objectives

By the terminate of this department, you will exist able to:

• Recognize the relation between the graph and the slope–intercept form of an equation of a line
• Identify the slope and y-intercept grade of an equation of a line
• Graph a line using its slope and intercept
• Choose the most convenient method to graph a line
• Graph and interpret applications of slope–intercept
• Apply slopes to place parallel lines
• Use slopes to identify perpendicular lines

Be Prepared 4.10

Before y'all become started, have this readiness quiz.

Add: $\frac{x}{\mathrm{four}}+\frac{1}{4}.$
If yous missed this trouble, review Example 1.77.

Be Prepared 4.11

Notice the reciprocal of $\frac{3}{7}.$
If you missed this problem, review Instance ane.70.

Be Prepared iv.12

Solve $\mathrm{two}x-\mathrm{iii}y=12\text{for}y$ .
If you lot missed this problem, review Example two.63.

Recognize the Relation Between the Graph and the Slope–Intercept Form of an Equation of a Line

We have graphed linear equations by plotting points, using intercepts, recognizing horizontal and vertical lines, and using the point–slope method. Once we see how an equation in slope–intercept grade and its graph are related, we'll have one more method we tin apply to graph lines.

In Graph Linear Equations in Two Variables, nosotros graphed the line of the equation $y=\frac{1}{\mathrm{ii}}x+\mathrm{three}$ past plotting points. See Effigy 4.24. Let's detect the slope of this line.

Figure 4.24

The red lines prove us the ascent is 1 and the run is 2. Substituting into the slope formula:

$$\begin{array}{ccc}\hfill m& =\hfill & \frac{\text{rising}}{\text{run}}\hfill \\ \hfill \mathrm{1000}& =\hfill & \frac{1}{2}\hfill \end{array}$$

What is the y-intercept of the line? The y-intercept is where the line crosses the y-axis, so y-intercept is $\left(0,3\right)$ . The equation of this line is:

Observe, the line has:

When a linear equation is solved for $y$ , the coefficient of the $x$ term is the gradient and the constant term is the y-coordinate of the y-intercept. We say that the equation $y=\frac{\mathrm{i}}{2}\mathrm{ten}+3$ is in slope–intercept form.

Gradient-Intercept Form of an Equation of a Line

The slope–intercept form of an equation of a line with slope $m$ and y-intercept, $\left(0,b\right)$ is,

$$y=\mathrm{chiliad}\mathrm{ten}+b$$

Sometimes the slope–intercept form is called the "y-form."

Example iv.40

Utilize the graph to find the slope and y-intercept of the line, $y=\mathrm{ii}x+1$ .

Compare these values to the equation $y=mx+b$ .

Try It 4.79

Use the graph to discover the slope and y-intercept of the line $y=\frac{\mathrm{two}}{\mathrm{iii}}\mathrm{ten}-1$ . Compare these values to the equation $y=mx+b$ .

Try It 4.80

Use the graph to discover the slope and y-intercept of the line $y=\frac{1}{2}x+\mathrm{three}$ . Compare these values to the equation $y=mx+b$ .

Identify the Slope and y-Intercept From an Equation of a Line

In Sympathise Slope of a Line, we graphed a line using the slope and a bespeak. When we are given an equation in slope–intercept form, nosotros tin can utilize the y-intercept as the point, and so count out the gradient from at that place. Permit's practice finding the values of the slope and y-intercept from the equation of a line.

Example 4.41

Identify the slope and y-intercept of the line with equation $y=\mathrm{-3}\mathrm{ten}+\mathrm{v}$ .

Try It 4.81

Identify the slope and y-intercept of the line $y=\frac{2}{5}x-1$ .

Try Information technology 4.82

Place the slope and y-intercept of the line $y=-\frac{4}{\mathrm{three}}\mathrm{10}+1$ .

When an equation of a line is not given in slope–intercept form, our commencement step will exist to solve the equation for $y$ .

Instance 4.42

Identify the gradient and y-intercept of the line with equation $\mathrm{10}+2y=6$ .

Try It 4.83

Identify the slope and y-intercept of the line $\mathrm{ten}+4y=8$ .

Attempt It four.84

Identify the slope and y-intercept of the line $3x+2y=12$ .

Graph a Line Using its Gradient and Intercept

Now that we know how to find the slope and y-intercept of a line from its equation, nosotros can graph the line by plotting the y-intercept and and so using the slope to find some other point.

Example 4.43

How to Graph a Line Using its Slope and Intercept

Graph the line of the equation $y=4\mathrm{ten}-2$ using its slope and y-intercept.

Try Information technology 4.85

Graph the line of the equation $y=4x+1$ using its slope and y-intercept.

Try It iv.86

Graph the line of the equation $y=\mathrm{ii}x-\mathrm{three}$ using its slope and y-intercept.

How To

Graph a line using its gradient and y-intercept.

1. Step ane. Find the slope-intercept class of the equation of the line.
2. Step ii. Identify the gradient and y-intercept.
3. Stride 3. Plot the y-intercept.
4. Stride 4. Use the slope formula $\mathrm{one\; thousand}=\frac{\text{rise}}{\text{run}}$ to identify the rise and the run.
5. Step 5. Starting at the y-intercept, count out the rising and run to mark the second point.
6. Pace 6. Connect the points with a line.

Case 4.44

Graph the line of the equation $y=\text{−}\mathrm{10}+4$ using its gradient and y-intercept.

Endeavour It four.87

Graph the line of the equation $y=\text{−}x-\mathrm{three}$ using its slope and y-intercept.

Attempt It 4.88

Graph the line of the equation $y=\text{−}\mathrm{ten}-1$ using its slope and y-intercept.

Instance 4.45

Graph the line of the equation $y=-\frac{\mathrm{ii}}{\mathrm{iii}}\mathrm{10}-3$ using its slope and y-intercept.

Effort Information technology 4.89

Graph the line of the equation $y=-\frac{5}{\mathrm{two}}x+1$ using its slope and y-intercept.

Endeavour It 4.xc

Graph the line of the equation $y=-\frac{3}{4}x-2$ using its gradient and y-intercept.

Example 4.46

Graph the line of the equation $4\mathrm{10}-3y=12$ using its slope and y-intercept.

Try Information technology four.91

Graph the line of the equation $2x-y=6$ using its slope and y-intercept.

Try It iv.92

Graph the line of the equation $\mathrm{iii}x-2y=8$ using its slope and y-intercept.

We take used a grid with $\mathrm{10}$ and $y$ both going from about $\mathrm{-x}$ to 10 for all the equations we've graphed so far. Not all linear equations tin be graphed on this small grid. Frequently, especially in applications with existent-earth data, we'll need to extend the axes to bigger positive or smaller negative numbers.

Instance 4.47

Graph the line of the equation $y=0.2\mathrm{10}+45$ using its slope and y-intercept.

Attempt It 4.93

Graph the line of the equation $y=\mathrm{0.five}\mathrm{ten}+25$ using its slope and y-intercept.

Attempt It 4.94

Graph the line of the equation $y=0.1x-\mathrm{xxx}$ using its slope and y-intercept.

Now that we accept graphed lines by using the slope and y-intercept, let's summarize all the methods we have used to graph lines. See Effigy 4.25.

Figure 4.25

Choose the Almost Convenient Method to Graph a Line

Now that we accept seen several methods nosotros can use to graph lines, how practice we know which method to use for a given equation?

While nosotros could plot points, apply the slope–intercept form, or discover the intercepts for any equation, if we recognize the most user-friendly way to graph a certain type of equation, our work will be easier. More often than not, plotting points is not the most efficient way to graph a line. We saw better methods in sections four.3, 4.4, and earlier in this section. Permit'southward look for some patterns to aid determine the virtually convenient method to graph a line.

Here are half-dozen equations we graphed in this chapter, and the method we used to graph each of them.

$$\begin{array}{cccccccc}& & & \mathbf{\text{Equation}}\hfill & & & & \mathbf{\text{Method}}\hfill \\ \text{\#1}\hfill & & & x=2\hfill & & & & \text{Vertical line}\hfill \\ \text{\#two}\hfill & & & y=\mathrm{iv}\hfill & & & & \text{Horizontal line}\hfill \\ \text{\#iii}\hfill & & & \text{−}x+\mathrm{ii}y=6\hfill & & & & \text{Intercepts}\hfill \\ \text{\#4}\hfill & & & \mathrm{iv}x-3y=12\hfill & & & & \text{Intercepts}\hfill \\ \text{\#v}\hfill & & & y=4x-2\hfill & & & & \text{Gradient–intercept}\hfill \\ \text{\#half dozen}\hfill & & & y=\text{−}x+\mathrm{four}\hfill & & & & \text{Slope–intercept}\hfill \end{array}$$

Equations #1 and #2 each take just one variable. Call back, in equations of this form the value of that one variable is constant; it does not depend on the value of the other variable. Equations of this course have graphs that are vertical or horizontal lines.

In equations #iii and #iv, both $x$ and $y$ are on the aforementioned side of the equation. These two equations are of the form $Ax+By=C$ . We substituted $y=0$ to find the x-intercept and $x=0$ to detect the y-intercept, then constitute a third indicate by choosing another value for $x$ or $y$ .

Equations #5 and #vi are written in gradient–intercept form. Afterward identifying the slope and y-intercept from the equation we used them to graph the line.

This leads to the post-obit strategy.

Strategy for Choosing the Most User-friendly Method to Graph a Line

Consider the form of the equation.

• If it simply has one variable, it is a vertical or horizontal line.
  • $x=a$ is a vertical line passing through the x-centrality at $a$.
  • $y=b$ is a horizontal line passing through the y-axis at $b$.
• If $y$ is isolated on i side of the equation, in the form $y=\mathrm{yard}\mathrm{10}+b$, graph by using the slope and y-intercept.
  • Place the gradient and y-intercept and then graph.
• If the equation is of the grade $A\mathrm{ten}+By=C$, discover the intercepts.
  • Find the x- and y-intercepts, a tertiary bespeak, and then graph.

Example 4.48

Make up one's mind the most convenient method to graph each line.

ⓐ $y=\mathrm{-6}$ ⓑ $5x-\mathrm{three}y=15$ ⓒ $x=7$ ⓓ $y=\frac{2}{\mathrm{v}}\mathrm{ten}-1$ .

Attempt Information technology four.95

Make up one's mind the about convenient method to graph each line: ⓐ $3x+2y=12$ ⓑ $y=4$ ⓒ $y=\frac{\mathrm{i}}{5}x-\mathrm{iv}$ ⓓ $\mathrm{10}=\mathrm{-vii}$ .

Attempt It 4.96

Determine the almost convenient method to graph each line: ⓐ $\mathrm{10}=6$ ⓑ $y=-\frac{3}{4}x+1$ ⓒ $y=\mathrm{-8}$ ⓓ $4\mathrm{10}-3y=\mathrm{-one}$ .

Graph and Interpret Applications of Slope–Intercept

Many real-world applications are modeled by linear equations. We will have a look at a few applications here so you can see how equations written in slope–intercept form chronicle to real-world situations.

Usually when a linear equation models a real-world state of affairs, dissimilar messages are used for the variables, instead of x and y. The variable names remind us of what quantities are being measured.

Example 4.49

The equation $F=\frac{9}{5}C+32$ is used to convert temperatures, $C$ , on the Celsius scale to temperatures, $F$ , on the Fahrenheit scale.

ⓐ Detect the Fahrenheit temperature for a Celsius temperature of 0.
ⓑ Find the Fahrenheit temperature for a Celsius temperature of twenty.
ⓒ Translate the slope and F-intercept of the equation.
ⓓ Graph the equation.

Try Information technology 4.97

The equation $h=\mathrm{two}s+\mathrm{l}$ is used to estimate a woman's height in inches, h, based on her shoe size, s.

1. ⓐ Estimate the height of a child who wears women's shoe size 0.
2. ⓑ Estimate the height of a woman with shoe size viii.
3. ⓒ Interpret the slope and h-intercept of the equation.
4. ⓓ Graph the equation.

Try It 4.98

The equation $T=\frac{\mathrm{one}}{4}\mathrm{due\; north}+\mathrm{xl}$ is used to estimate the temperature in degrees Fahrenheit, T, based on the number of cricket chirps, n, in 1 minute.

1. ⓐEstimate the temperature when there are no chirps.
2. ⓑ Estimate the temperature when the number of chirps in one minute is 100.
3. ⓒ Translate the slope and T-intercept of the equation.
4. ⓓ Graph the equation.

The cost of running some types business has two components—a stock-still cost and a variable cost. The fixed cost is ever the same regardless of how many units are produced. This is the toll of hire, insurance, equipment, advertising, and other items that must exist paid regularly. The variable price depends on the number of units produced. It is for the cloth and labor needed to produce each item.

Example 4.50

Stella has a home business organisation selling gourmet pizzas. The equation $C=4p+25$ models the relation betwixt her weekly cost, C, in dollars and the number of pizzas, p, that she sells.

ⓐ Find Stella's cost for a week when she sells no pizzas.
ⓑ Detect the cost for a week when she sells 15 pizzas.
ⓒ Interpret the slope and C-intercept of the equation.
ⓓ Graph the equation.

Try It 4.99

Sam drives a delivery van. The equation $C=0.5\mathrm{thousand}+60$ models the relation between his weekly price, C, in dollars and the number of miles, yard, that he drives.

ⓐ Observe Sam's cost for a calendar week when he drives 0 miles.
ⓑ Observe the cost for a week when he drives 250 miles.
ⓒ Translate the gradient and C-intercept of the equation.
ⓓ Graph the equation.

Try It four.100

Loreen has a calligraphy business. The equation $C=1.8\mathrm{north}+35$ models the relation between her weekly cost, C, in dollars and the number of wedding invitations, n, that she writes.

1. ⓐObserve Loreen's cost for a calendar week when she writes no invitations.
2. ⓑ Notice the cost for a week when she writes 75 invitations.
3. ⓒ Interpret the slope and C-intercept of the equation.
4. ⓓ Graph the equation.

Use Slopes to Place Parallel Lines

The gradient of a line indicates how steep the line is and whether it rises or falls as we read information technology from left to right. Two lines that accept the same slope are chosen parallel lines. Parallel lines never intersect.

We say this more than formally in terms of the rectangular coordinate system. Two lines that accept the same slope and different y-intercepts are called parallel lines. Meet Figure four.27.

Figure 4.27 Verify that both lines take the same slope, $m=\frac{2}{5}$, and dissimilar y-intercepts.

What virtually vertical lines? The slope of a vertical line is undefined, and then vertical lines don't fit in the definition to a higher place. We say that vertical lines that take different x-intercepts are parallel. See Figure 4.28.

Figure 4.28 Vertical lines with diferent x-intercepts are parallel.

Parallel Lines

Parallel lines are lines in the same plane that practise non intersect.

• Parallel lines have the same slope and dissimilar y-intercepts.
• If $g_{\mathrm{i}}$ and $k_2$ are the slopes of two parallel lines and then$m_{\mathrm{i}}=m_{\mathrm{two}}$.
• Parallel vertical lines have different ten-intercepts.

Allow's graph the equations $y=\mathrm{-ii}x+\mathrm{three}$ and $2\mathrm{10}+y=\mathrm{-1}$ on the same filigree. The first equation is already in slope–intercept form: $y=\mathrm{-2}x+\mathrm{three}$ . We solve the second equation for $y$ :

$$\begin{array}{ccc}\hfill 2x+y& =\hfill & \mathrm{-1}\hfill \\ \hfill y& =\hfill & \mathrm{-2}x-1\hfill \end{array}$$

Graph the lines.

Notice the lines look parallel. What is the slope of each line? What is the y-intercept of each line?

$$\begin{array}{cccccccccc}\hfill y& =\hfill & m\mathrm{10}+b\hfill & & & & & \hfill y& =\hfill & mx+b\hfill \\ \hfill y& =\hfill & \mathrm{-2}\mathrm{ten}+\mathrm{three}\hfill & & & & & \hfill y& =\hfill & \mathrm{-ii}\mathrm{10}-1\hfill \\ \hfill m& =\hfill & \mathrm{-2}\hfill & & & & & \hfill m& =\hfill & \mathrm{-2}\hfill \\ \hfill b& =\hfill & 3,\text{(0, 3)}\hfill & & & & & \hfill b& =\hfill & \mathrm{-1},\text{(0, −i)}\hfill \end{array}$$

The slopes of the lines are the same and the y-intercept of each line is different. So nosotros know these lines are parallel.

Since parallel lines have the aforementioned gradient and unlike y-intercepts, we can at present just look at the slope–intercept class of the equations of lines and make up one's mind if the lines are parallel.

Example four.51

Use slopes and y-intercepts to determine if the lines $\mathrm{iii}x-2y=\mathrm{vi}$ and $y=\frac{3}{2}x+\mathrm{i}$ are parallel.

Try It four.101

Apply slopes and y-intercepts to determine if the lines $2x+5y=\mathrm{five}\text{and}y=-\frac{2}{5}\mathrm{ten}-4$ are parallel.

Try It 4.102

Utilise slopes and y-intercepts to decide if the lines $\mathrm{four}\mathrm{10}-3y=6\text{and}y=\frac{4}{3}\mathrm{10}-1$ are parallel.

Example 4.52

Use slopes and y-intercepts to decide if the lines $y=\mathrm{-4}$ and $y=3$ are parallel.

Effort It 4.103

Utilize slopes and y-intercepts to make up one's mind if the lines $y=8\text{and}y=\mathrm{-half\; dozen}$ are parallel.

Try It 4.104

Use slopes and y-intercepts to determine if the lines $y=1\text{and}y=\mathrm{-5}$ are parallel.

Example 4.53

Employ slopes and y-intercepts to determine if the lines $x=\mathrm{-two}$ and $\mathrm{10}=\mathrm{-5}$ are parallel.

Try Information technology 4.105

Utilize slopes and y-intercepts to decide if the lines $\mathrm{10}=1$ and $x=\mathrm{-v}$ are parallel.

Effort Information technology 4.106

Use slopes and y-intercepts to determine if the lines $x=8$ and $\mathrm{ten}=\mathrm{-half\; dozen}$ are parallel.

Case 4.54

Use slopes and y-intercepts to decide if the lines $y=2x-\mathrm{iii}$ and $\mathrm{-vi}x+3y=\mathrm{-nine}$ are parallel. You may want to graph these lines, too, to see what they look similar.

Try It 4.107

Use slopes and y-intercepts to decide if the lines $y=-\frac{1}{\mathrm{ii}}x-1$ and $\mathrm{10}+2y=\mathrm{two}$ are parallel.

Try It four.108

Utilise slopes and y-intercepts to decide if the lines $y=\frac{3}{4}\mathrm{ten}-3$ and $3x-4y=12$ are parallel.

Employ Slopes to Identify Perpendicular Lines

Permit's look at the lines whose equations are $y=\frac{1}{4}\mathrm{10}-1$ and $y=\mathrm{-four}\mathrm{10}+2$ , shown in Figure four.29.

Figure four.29

These lines lie in the same plane and intersect in correct angles. We telephone call these lines perpendicular.

What do yous notice almost the slopes of these two lines? As we read from left to right, the line $y=\frac{\mathrm{i}}{4}x-1$ rises, so its slope is positive. The line $y=\mathrm{-four}\mathrm{ten}+\mathrm{ii}$ drops from left to correct, so it has a negative slope. Does information technology brand sense to you that the slopes of two perpendicular lines will have opposite signs?

If we look at the slope of the starting time line, $m_1=\frac{1}{\mathrm{four}}$ , and the gradient of the 2nd line, ${\mathrm{thou}}_2=\mathrm{-4}$ , we can see that they are negative reciprocals of each other. If we multiply them, their product is $\mathrm{-1}.$

$$\begin{array}{c}{\mathrm{1000}}_{\mathrm{ane}}·{\mathrm{thousand}}_2\hfill \\ \frac{\mathrm{i}}{4}\left(\mathrm{-4}\right)\hfill \\ -1\hfill \end{array}$$

This is always true for perpendicular lines and leads us to this definition.

Perpendicular Lines

Perpendicular lines are lines in the same plane that grade a right angle.

If ${\mathrm{grand}}_1\text{and}{\mathrm{thousand}}_{\mathrm{two}}$ are the slopes of two perpendicular lines, then:

$${\mathrm{one\; thousand}}_1·m_2=\mathrm{-ane}\text{and}{k}_{\mathrm{ane}}=\frac{\mathrm{-ane}}{m_2}$$

Vertical lines and horizontal lines are e'er perpendicular to each other.

We were able to look at the slope–intercept form of linear equations and decide whether or non the lines were parallel. Nosotros tin can practise the same thing for perpendicular lines.

We find the slope–intercept form of the equation, and and so meet if the slopes are negative reciprocals. If the product of the slopes is $\mathrm{-1}$ , the lines are perpendicular. Perpendicular lines may have the same y-intercepts.

Instance 4.55

Utilize slopes to make up one's mind if the lines, $y=\mathrm{-v}\mathrm{10}-4$ and $\mathrm{10}-5y=5$ are perpendicular.

Try Information technology 4.109

Use slopes to determine if the lines $y=\mathrm{-three}\mathrm{10}+2$ and $x-\mathrm{iii}y=4$ are perpendicular.

Endeavour It 4.110

Apply slopes to decide if the lines $y=2\mathrm{ten}-5$ and $x+2y=\mathrm{-six}$ are perpendicular.

Example 4.56

Use slopes to determine if the lines, $\mathrm{vii}x+2y=3$ and $2x+7y=5$ are perpendicular.

Try It 4.111

Utilize slopes to decide if the lines $5x+4y=1$ and $\mathrm{four}x+\mathrm{five}y=3$ are perpendicular.

Try It four.112

Employ slopes to decide if the lines $2x-\mathrm{ix}y=3$ and $9x-\mathrm{ii}y=\mathrm{one}$ are perpendicular.

Section 4.5 Exercises

Practice Makes Perfect

Recognize the Relation Betwixt the Graph and the Slope–Intercept Course of an Equation of a Line

In the following exercises, utilize the graph to find the slope and y-intercept of each line. Compare the values to the equation $y=\mathrm{thou}x+b$ .

288 .

$y=3x-\mathrm{five}$

289.

$y=4x-2$

290 .

$y=\text{−}\mathrm{10}+4$

291.

$y=\mathrm{-3}x+1$

292 .

$y=-\frac{\mathrm{four}}{3}\mathrm{10}+\mathrm{ane}$

293.

$y=-\frac{2}{\mathrm{v}}x+3$

Identify the Gradient and y-Intercept From an Equation of a Line

In the following exercises, identify the slope and y-intercept of each line.

294 .

$y=\mathrm{-7}x+\mathrm{iii}$

295.

$y=\mathrm{-ix}x+7$

296 .

$y=6x-\mathrm{viii}$

297.

$y=4x-\mathrm{ten}$

298 .

$3x+y=5$

299.

$4x+y=8$

300 .

$6x+4y=12$

301.

$\mathrm{eight}x+\mathrm{iii}y=12$

302 .

$\mathrm{five}\mathrm{10}-\mathrm{ii}y=\mathrm{vi}$

303.

$7x-\mathrm{iii}y=9$

Graph a Line Using Its Slope and Intercept

In the following exercises, graph the line of each equation using its slope and y-intercept.

306 .

$y=3x-1$

307.

$y=\mathrm{two}\mathrm{10}-3$

308 .

$y=\text{−}x+\mathrm{ii}$

309.

$y=\text{−}x+3$

310 .

$y=\text{−}x-\mathrm{four}$

311.

$y=\text{−}x-\mathrm{ii}$

312 .

$y=-\frac{3}{\mathrm{four}}x-1$

313.

$y=-\frac{2}{5}\mathrm{10}-\mathrm{three}$

314 .

$y=-\frac{3}{5}x+2$

315.

$y=-\frac{2}{3}\mathrm{ten}+1$

316 .

$3\mathrm{10}-4y=8$

317.

$\mathrm{four}x-3y=6$

318 .

$y=0.1x+15$

319.

$y=0.3x+25$

Choose the Near Convenient Method to Graph a Line

In the following exercises, determine the about convenient method to graph each line.

324 .

$y=\mathrm{-3}x+\mathrm{four}$

325.

$y=\mathrm{-5}\mathrm{10}+2$

328 .

$y=\frac{\mathrm{two}}{3}x-1$

329.

$y=\frac{4}{5}x-3$

332 .

$3x-\mathrm{ii}y=\mathrm{-12}$

333.

$2x-5y=\mathrm{-x}$

334 .

$y=-\frac{1}{4}x+\mathrm{three}$

335.

$y=-\frac{\mathrm{i}}{3}x+5$

Graph and Interpret Applications of Slope–Intercept

336 .

The equation $P=31+1.75\mathrm{west}$ models the relation betwixt the amount of Tuyet's monthly water bill payment, P, in dollars, and the number of units of water, w, used.

1. ⓐ Find Tuyet'south payment for a month when 0 units of water are used.
2. ⓑ Find Tuyet's payment for a month when 12 units of water are used.
3. ⓒ Interpret the gradient and P-intercept of the equation.
4. ⓓ Graph the equation.

337.

The equation $P=28+2.54\mathrm{westward}$ models the relation between the amount of Randy'due south monthly h2o neb payment, P, in dollars, and the number of units of h2o, west, used.

1. ⓐ Detect the payment for a calendar month when Randy used 0 units of water.
2. ⓑ Find the payment for a calendar month when Randy used 15 units of water.
3. ⓒ Translate the slope and P-intercept of the equation.
4. ⓓ Graph the equation.

338 .

Bruce drives his car for his job. The equation $R=0.575m+42$ models the relation betwixt the amount in dollars, R, that he is reimbursed and the number of miles, 1000, he drives in i day.

1. ⓐ Find the amount Bruce is reimbursed on a day when he drives 0 miles.
2. ⓑ Find the amount Bruce is reimbursed on a solar day when he drives 220 miles.
3. ⓒ Interpret the slope and R-intercept of the equation.
4. ⓓ Graph the equation.

339.

Janelle is planning to rent a motorcar while on vacation. The equation $C=0.32\mathrm{thou}+15$ models the relation between the price in dollars, C, per mean solar day and the number of miles, m, she drives in one day.

1. ⓐ Find the cost if Janelle drives the car 0 miles 1 day.
2. ⓑ Find the cost on a solar day when Janelle drives the automobile 400 miles.
3. ⓒ Interpret the slope and C–intercept of the equation.
4. ⓓ Graph the equation.

340 .

Cherie works in retail and her weekly salary includes committee for the amount she sells. The equation $\mathrm{Due\; south}=400+0.15c$ models the relation between her weekly bacon, South, in dollars and the corporeality of her sales, c, in dollars.

1. ⓐ Discover Cherie's salary for a calendar week when her sales were 0.
2. ⓑ Find Cherie's salary for a week when her sales were 3600.
3. ⓒ Interpret the slope and S–intercept of the equation.
4. ⓓ Graph the equation.

341.

Patel'due south weekly salary includes a base pay plus committee on his sales. The equation $\mathrm{South}=750+0.09c$ models the relation between his weekly salary, S, in dollars and the amount of his sales, c, in dollars.

1. ⓐ Find Patel'southward salary for a week when his sales were 0.
2. ⓑ Notice Patel'southward salary for a calendar week when his sales were 18,540.
3. ⓒ Interpret the slope and S-intercept of the equation.
4. ⓓ Graph the equation.

342 .

Costa is planning a lunch banquet. The equation $C=450+28g$ models the relation between the toll in dollars, C, of the banquet and the number of guests, g.

1. ⓐ Observe the cost if the number of guests is 40.
2. ⓑ Find the cost if the number of guests is lxxx.
3. ⓒ Interpret the slope and C-intercept of the equation.
4. ⓓ Graph the equation.

343.

Margie is planning a dinner banquet. The equation $C=750+42\mathrm{thou}$ models the relation between the cost in dollars, C of the feast and the number of guests, g.

1. ⓐ Find the price if the number of guests is 50.
2. ⓑ Discover the cost if the number of guests is 100.
3. ⓒ Interpret the gradient and C–intercept of the equation.
4. ⓓ Graph the equation.

Employ Slopes to Place Parallel Lines

In the post-obit exercises, use slopes and y-intercepts to determine if the lines are parallel.

344 .

$y=\frac{3}{\mathrm{four}}x-3;3x-\mathrm{iv}y=-2$

345.

$y=\frac{2}{3}x-\mathrm{i};2x-3y=-2$

346 .

$2x-5y=-\mathrm{three};y=\frac{\mathrm{ii}}{\mathrm{five}}x+1$

347.

$3x-\mathrm{iv}y=-\mathrm{two};y=\frac{3}{4}x-3$

348 .

$2x-4y=6;\mathrm{10}-2y=3$

349.

$\mathrm{half-dozen}x-\mathrm{three}y=9;2\mathrm{10}-y=3$

350 .

$4\mathrm{ten}+\mathrm{ii}y=6;6\mathrm{10}+3y=3$

351.

$8x+\mathrm{vi}y=6;12x+9y=12$

360 .

$x-y=2;2x-2y=4$

361.

$\mathrm{four}x+4y=8;x+y=\mathrm{two}$

362 .

$\mathrm{ten}-3y=6;2\mathrm{10}-6y=12$

363.

$5x-2y=11;5\mathrm{ten}-y=\mathrm{seven}$

364 .

$3x-\mathrm{vi}y=12;\mathrm{six}x-3y=3$

365.

$4x-\mathrm{viii}y=16;x-2y=4$

366 .

$\mathrm{ix}x-\mathrm{three}y=6;3\mathrm{10}-y=2$

367.

$\mathrm{10}-5y=\mathrm{x};\mathrm{five}x-y=-\mathrm{ten}$

368 .

$\mathrm{vii}\mathrm{10}-\mathrm{four}y=\mathrm{eight};4x+7y=\mathrm{xiv}$

369.

$\mathrm{ix}\mathrm{ten}-\mathrm{five}y=4;5x+\mathrm{ix}y=-1$

Use Slopes to Place Perpendicular Lines

In the following exercises, utilize slopes and y-intercepts to determine if the lines are perpendicular.

370 .

$3x-2y=\mathrm{viii};\mathrm{ii}x+3y=\mathrm{six}$

371.

$x-4y=8;4x+y=\mathrm{ii}$

372 .

$2\mathrm{10}+\mathrm{five}y=3;5x-2y=6$

373.

$2\mathrm{10}+3y=5;3x-2y=\mathrm{seven}$

374 .

$3\mathrm{ten}-2y=1;\mathrm{ii}x-3y=\mathrm{ii}$

375.

$3x-4y=8;\mathrm{iv}x-3y=6$

376 .

$5x+2y=\mathrm{half\; dozen};2\mathrm{10}+5y=8$

377.

$2x+4y=3;\mathrm{half-dozen}x+3y=\mathrm{ii}$

378 .

$4x-2y=5;3\mathrm{10}+6y=8$

379.

$2x-\mathrm{six}y=\mathrm{iv};12\mathrm{10}+\mathrm{iv}y=\mathrm{nine}$

380 .

$\mathrm{half\; dozen}\mathrm{10}-4y=5;8\mathrm{ten}+12y=\mathrm{three}$

381.

$\mathrm{eight}x-\mathrm{two}y=7;\mathrm{iii}\mathrm{ten}+12y=9$

Everyday Math

382 .

The equation $C=\frac{5}{9}F-\mathrm{17.eight}$ tin be used to convert temperatures F, on the Fahrenheit calibration to temperatures, C, on the Celsius calibration.

1. ⓐ Explain what the gradient of the equation means.
2. ⓑ Explain what the C–intercept of the equation means.

383.

The equation $\mathrm{northward}=\mathrm{four}T-160$ is used to estimate the number of cricket chirps, n, in i infinitesimal based on the temperature in degrees Fahrenheit, T.

1. ⓐ Explicate what the gradient of the equation means.
2. ⓑ Explain what the due north–intercept of the equation means. Is this a realistic situation?

Writing Exercises

384 .

Explicate in your own words how to determine which method to use to graph a line.

385.

Why are all horizontal lines parallel?

Self Check

ⓐ Afterwards completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

ⓑ Later looking at the checklist, do you call back yous are well-prepared for the next section? Why or why non?

Lesson 4.2 Understanding Slope-intercept Form,

Source: https://openstax.org/books/elementary-algebra-2e/pages/4-5-use-the-slope-intercept-form-of-an-equation-of-a-line

Posted by: karstenexiligh.blogspot.com

Share this post