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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

Answers

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?

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