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, equals, start color #ed5fa6, m, end color #ed5fa6, x, plus, start color #1fab54, b, end color #1fab54
When an equation is written in this form, start color #ed5fa6, m, end color #ed5fa6 gives the slope of the line and start color #1fab54, b, end color #1fab54 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 start color #ed5fa6, minus, 1, end color #ed5fa6 and y-intercept is left parenthesis, 0, comma, start color #1fab54, 5, end color #1fab54, right parenthesis. Well, we simply plug start color #ed5fa6, m, equals, minus, 1, end color #ed5fa6 and start color #1fab54, b, equals, 5, end color #1fab54 into slope-intercept form!
y, equals, start color #ed5fa6, minus, 1, end color #ed5fa6, x, start color #1fab54, plus, 5, end color #1fab54

Example 2: Equation from two points

Suppose we want to find the line that passes through the points left parenthesis, 0, comma, minus, 4, right parenthesis and left parenthesis, 3, comma, minus, 1, right parenthesis. First, we notice that left parenthesis, 0, comma, start color #1fab54, minus, 4, end color #1fab54, right parenthesis is the y-intercept. Second, we use the two points to find the slope:
Now we can write the equation in slope-intercept:
y, equals, start color #ed5fa6, 1, end color #ed5fa6, x, start color #1fab54, minus, 4, end color #1fab54
Problem 1
Write the equation of the line whose slope is 5 and y-intercept is left parenthesis, 0, comma, minus, 7, right parenthesis.
y, equals

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, equals, start color #ed5fa6, 2, end color #ed5fa6, x, start color #1fab54, plus, 3, end color #1fab54. We can quickly tell that the corresponding line has a slope of start color #ed5fa6, 2, end color #ed5fa6 and its y-intercept is left parenthesis, 0, comma, start color #1fab54, 3, end color #1fab54, right parenthesis. Now we can graph the line:
A coordinate plane. The x- and y-axes each scale by one. The equation y equals two x plus three is graphed and labeled. The points zero, three and one, five are plotted. There is a horizontal segment from zero, three to one, three that is labeled plus one. There is a vertical segment from one, three to one, five that is labeled plus two.
Problem 1
What is the slope of the line y, equals, 3, x, minus, 1?
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text
What is the y-intercept of the line?
left parenthesis, 0, comma
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text
right parenthesis

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

Want to join the conversation?