<img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" />
Skip Navigation

Graphs Using Slope-Intercept Form

Use the y-intercept and the 'rise over run' to graph a line

Atoms Practice
Practice Graphs Using Slope-Intercept Form
Practice Now
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.


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 yintercept. From these two pieces of information we can graph any line.

Example A

Graph y=13x+4 on the Cartesian plane.

Solution: First, the Cartesian plane is the xy plane. Typically, when graphing lines, draw each axis from -10 to 10. To graph this line, you need to find the slope and yintercept. By looking at the equation, 13 is the slope and 4, or (0, 4), is the yintercept. To start graphing this line, plot the yintercept on the yaxis.

Now, we need to use the slope to find the next point on the line. Recall that the slope is also riserun, so for 13, we will rise 1 and run 3 from the yintercept. 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=13x+4.

Example B

Graph y=4x5.

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 yintercept, 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 xaxis. 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 yaxis 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=34x1

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 yaxis and draw a horizontal line.

Explore More

Graph the following lines in the Cartesian plane.

  1. y=2x3
  2. y=x+4
  3. y=13x1
  4. y=9
  5. y=25x+7
  6. y=24x5
  7. y=5x2
  8. y=x
  9. y=4
  10. x=3
  11. y=32x+3
  12. y=16x8
  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?


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.

Image Attributions


Please wait...
Please wait...

Original text