If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Main content

Slope-intercept form review

Review slope-intercept form and how to use it to solve problems.

What is slope-intercept form?

Slope-intercept is a specific form of linear equations in two variables:
y=mx+b
When an equation is written in this form, m gives the slope of the line and b gives its y-intercept.
Want to learn more about slope-intercept form? Check out this video.

Finding slope-intercept equation from features or graph

Example 1: Equation from slope and intercept

Suppose we want to find the equation of the line whose slope is 1 and y-intercept is (0,5). Well, we simply plug m=1 and b=5 into slope-intercept form!
y=1x+5

Example 2: Equation from two points

Suppose we want to find the line that passes through the points (0,4) and (3,1). First, we notice that (0,4) is the y-intercept. Second, we use the two points to find the slope:
Slope=1(4)30 =33=1
Now we can write the equation in slope-intercept:
y=1x4
Problem 1
Write the equation of the line whose slope is 5 and y-intercept is (0,7).
y=

Want to try more problems like this? Check out these exercises:

Finding features and graph from slope-intercept equation

When we have a linear equation in slope-intercept form, we can quickly find the slope and y-intercept of the corresponding line. This also allows us to graph it.
Consider, for example, the equation y=2x+3. We can quickly tell that the corresponding line has a slope of 2 and its y-intercept is (0,3). Now we can graph the line:
Problem 1
What is the slope of the line y=3x1?
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
What is the y-intercept of the line?
(0,
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
)

Want to try more problems like this? Check out these exercises: