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

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 greenD, minus, 4, end color greenD, 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 maroonC, 1, end color maroonC, x, start color greenD, minus, 4, end color greenD
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 maroonC, 2, end color maroonC, x, start color greenD, plus, 3, end color greenD. We can quickly tell that the corresponding line has a slope of start color maroonC, 2, end color maroonC and its y-intercept is left parenthesis, 0, comma, start color greenD, 3, end color greenD, right parenthesis. Now we can graph the line:
Problem 1
What is the slope of the line y, equals, 3, x, minus, 1?
  • Dit svar bør være
  • et heltal, som 6
  • en forkortet, ægte brøk, som eksempelvis 3, slash, 5
  • en forkortet, uægte brøk, som eksempelvis 7, slash, 4
  • et blandet tal, som eksempelvis 1, space, 3, slash, 4
  • et præcist decimaltal, som eksempelvis 0, point, 75
  • et multiplum af pi, som f.eks. 12, space, p, i eller 2, slash, 3, space, p, i
What is the y-intercept of the line?
left parenthesis, 0, comma
  • Dit svar bør være
  • et heltal, som 6
  • en forkortet, ægte brøk, som eksempelvis 3, slash, 5
  • en forkortet, uægte brøk, som eksempelvis 7, slash, 4
  • et blandet tal, som eksempelvis 1, space, 3, slash, 4
  • et præcist decimaltal, som eksempelvis 0, point, 75
  • et multiplum af pi, som f.eks. 12, space, p, i eller 2, slash, 3, space, p, i
right parenthesis

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