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4.9: Slope-Intercept Form

Difficulty Level: Basic Created by: CK-12
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Suppose that you were a senior in high school and wanted to graph a linear equation that could be used to find the number of days until graduation based on the day of the year. One way to graph such an equation would be to find the slope and yintercept, but how could you determine this information? The answer is by converting the equation into slope-intercept form, and in this Concept, you'll learn all about this form of a linear equation.


So, you have learned how to graph the solutions to an equation in two variables by making a table and by using its intercepts. A previous lesson introduced the formulas for slope. This lesson will combine intercepts and slope into a new formula.

You have seen different forms of this formula. Below are several examples.


The proper name given to each of these equations is slope-intercept form because each equation tells the slope and the yintercept of the line.

The slope-intercept form of an equation is: y=(slope)x+(yintercept).

y=(m)x+b, where m=slope and b=yintercept

This equation makes it quite easy to graph the solutions to an equation of two variables because it gives you two necessary values:

  1. The starting position of your graph (the yintercept)
  2. The directions to find your second coordinate (the slope)

Example A

Determine the slope and the yintercept of the first two equations in the opener of this Concept.

Solution: Using the definition of slope-intercept form; 2x+5=y has a slope of 2 and a yintercept of

(0, 5).

y=13x+11 has a slope of 13 and a yintercept of (0, 11).

Slope-intercept form applies to many equations, even those that do not look like the “standard” equation.

Example B

Determine the slope and yintercept of 7x=y.

Solution: At first glance, this does not look like the “standard” equation. However, we can substitute values for the slope and yintercept.


This means the slope is 7 and the yintercept is 0.

Example C

Determine the slope and yintercept of the lines graphed below.

Solution: Beginning with line a, you can easily see the graph crosses the yaxis (the yintercept) at (0, 5). From this point, find a second coordinate on the line crossing at a lattice point.

Line a: The yintercept is (0, 5). The line also passes through (2, 3).

slope m=yx=22=1

Line b: The yintercept is (0, 2). The line also passes through (1, 5).

slope m=yx=31=3

The remaining lines will be left for you in the Practice Set.

Guided Practice

Determine the slope and yintercept of y=5.


Using what you learned in the last Concept, the slope of every line of the form y=some number is zero because it is a horizontal line. Rewriting our original equation to fit slope-intercept form yields:


Therefore, the slope is zero and the yintercept is (0, 5).

You can also use a graph to determine the slope and yintercept of a line.


Sample explanations for some of the practice exercises below are available by viewing the following video. Note that there is not always a match between the number of the practice exercise in the video and the number of the practice exercise listed in the following exercise set. However, the practice exercise is the same in both. CK-12 Basic Algebra: Graphs Using Slope-Intercept Form (11:11)

In 1 – 8, identify the slope and yintercept for the equation.

  1. y=2x+5
  2. y=0.2x+7
  3. y=x
  4. y=3.75
  5. 23x9=y
  6. y=0.01x+10,000
  7. 7+35x=y
  8. 5x+12=20

In 9 – 15, identify the slope of the following lines.

  1. F
  2. C
  3. A
  4. G
  5. B
  6. D
  7. \begin{align*}E\end{align*}

In 16 – 21, identify the slope and \begin{align*}y-\end{align*}intercept for the following functions.

  1. \begin{align*}D\end{align*}
  2. \begin{align*}A\end{align*}
  3. \begin{align*}F\end{align*}
  4. \begin{align*}B\end{align*}
  5. \begin{align*}E\end{align*}
  6. \begin{align*}C\end{align*}

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lattice point

At the intersection of grid lines on a graph are lattice points. A lattice point is a coordinate pair with integer values.

slope-intercept form

y=(slope)x+(y-intercept) or y=(m)x+b, where m = slope and b = y-intercept.

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Difficulty Level:
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Feb 24, 2012
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