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# Graphs Using Slope-Intercept Form

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Practice Graphs Using Slope-Intercept Form
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Graph a Line in Slope-Intercept Form

The cost per month for a cell-phone plan is $60 plus$7.50 for every gigabyte (GB) of data you use. (For billing purposes, actual usage is rounded to the nearest one-quarter GB.) Write an equation for the cost of the data plan and determine how much your bill will be if you use 4.5 GB of data in a month.

### Guidance

From the previous lesson, we know that the equation of a line is $y = mx + b$ , where $m$ is the slope and $b$ is the $y-$ intercept. From these two pieces of information we can graph any line.

#### Example A

Graph $y = \frac{1}{3}x + 4$ on the Cartesian plane.

Solution: First, the Cartesian plane is the $x-y$ plane. Typically, when graphing lines, draw each axis from -10 to 10. To graph this line, you need to find the slope and $y-$ intercept. By looking at the equation, $\frac{1}{3}$ is the slope and 4, or (0, 4), is the $y-$ intercept. To start graphing this line, plot the $y-$ intercept on the $y-$ axis.

Now, we need to use the slope to find the next point on the line. Recall that the slope is also $\frac{rise}{run}$ , so for $\frac{1}{3}$ , we will rise 1 and run 3 from the $y-$ intercept. Do this a couple of times to get at least three points.

Now that we have three points, connect them to form the line $y = \frac{1}{3}x + 4$ .

#### Example B

Graph $y = -4x -5$ .

Solution: Now that the slope is negative, the vertical distance will “fall” instead of rise. Also, because the slope is a whole number, we need to put it over 1. Therefore, for a slope of -4, the line will fall 4 and run 1 OR rise 4 and run backward 1. Start at the $y-$ intercept, and then use the slope to find a few more points.

#### Example C

Graph $x = 5$ .

Solution: Any line in the form $x = a$ is a vertical line. To graph any vertical line, plot the value, in this case 5, on the $x-$ axis. Then draw the vertical line.

To graph a horizontal line, $y = b$ , it will be the same process, but plot the value given on the $y-$ axis and draw a horizontal line.

Intro Problem Revisit If x is the number of GB of data you use in a month and y is the total cost you pay, then the equation for the cell-phone plan would be $y=7.5x + 60$ . If you use 4.5 GB in a month, the total cost would be $y=7.5(4.5)+60=93.75$ .

So your bill for the month would be \$93.75.

### Guided Practice

Graph the following lines.

1. $y = -x + 2$

2. $y = \frac{3}{4}x - 1$

3. $y = -6$

All the answers are on the same grid below.

1. Plot (0, 2) and the slope is -1, which means you fall 1 and run 1.

2. Plot (0, -1) and then rise 3 and run 4 to the next point, (4, 2).

3. Plot -6 on the $y-$ axis and draw a horizontal line.

### Explore More

Graph the following lines in the Cartesian plane.

1. $y = -2x -3$
2. $y = x + 4$
3. $y = \frac{1}{3}x - 1$
4. $y = 9$
5. $y = - \frac{2}{5}x + 7$
6. $y = \frac{2}{4}x - 5$
7. $y = -5x -2$
8. $y = -x$
9. $y = 4$
10. $x = -3$
11. $y = \frac{3}{2}x + 3$
12. $y = - \frac{1}{6}x - 8$
13. Graph $y = 4$ and $x = -6$ on the same set of axes. Where do they intersect?
14. If you were to make a general rule for the lines $y = b$ and $x = a$ , where will they always intersect?
15. The cost per month, $C$ (in dollars), of placing an ad on a website is $C = 0.25x + 50$ , where $x$ is the number of times someone clicks on your link. How much would it cost you if 500 people clicked on your link?

### Vocabulary Language: English

Cartesian Plane

Cartesian Plane

The Cartesian plane is a grid formed by a horizontal number line and a vertical number line that cross at the (0, 0) point, called the origin.
linear equation

linear equation

A linear equation is an equation between two variables that produces a straight line when graphed.
Linear Function

Linear Function

A linear function is a relation between two variables that produces a straight line when graphed.
Slope-Intercept Form

Slope-Intercept Form

The slope-intercept form of a line is $y = mx + b,$ where $m$ is the slope and $b$ is the $y-$intercept.