4.9: SlopeIntercept Form
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
Guidance
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 slopeintercept form because each equation tells the slope and the
The slopeintercept form of an equation is:
This equation makes it quite easy to graph the solutions to an equation of two variables because it gives you two necessary values:
 The starting position of your graph (the
y− intercept)  The directions to find your second coordinate (the slope)
Example A
Determine the slope and the
Solution: Using the definition of slopeintercept form;
(0, 5).
Slopeintercept form applies to many equations, even those that do not look like the “standard” equation.
Example B
Determine the slope and
Solution: At first glance, this does not look like the “standard” equation. However, we can substitute values for the slope and
This means the slope is 7 and the
Example C
Determine the slope and
Solution: Beginning with line
Line
Line
The remaining lines will be left for you in the Practice Set.
Guided Practice
Determine the slope and
Solution:
Using what you learned in the last Concept, the slope of every line of the form
Therefore, the slope is zero and the
You can also use a graph to determine the slope and
Practice
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. CK12 Basic Algebra: Graphs Using SlopeIntercept Form (11:11)
In 1 – 8, identify the slope and

y=2x+5 
y=−0.2x+7 
y=x 
y=3.75 
23x−9=y 
y=−0.01x+10,000 
7+35x=y 
−5x+12=20
In 9 – 15, identify the slope of the following lines.

F 
C 
A 
G 
B 
D  \begin{align*}E\end{align*}
In 16 – 21, identify the slope and \begin{align*}y\end{align*}intercept for the following functions.
 \begin{align*}D\end{align*}
 \begin{align*}A\end{align*}
 \begin{align*}F\end{align*}
 \begin{align*}B\end{align*}
 \begin{align*}E\end{align*}
 \begin{align*}C\end{align*}
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Image Attributions
Here you'll learn how to convert a linear equation into slopeintercept form and determine the slope and @$\begin{align*}y\end{align*}@$intercept of the line.