4.10: Graphs Using SlopeIntercept Form
Suppose a company had the slope and \begin{align*}y\end{align*}
Guidance
Once we know the slope and the \begin{align*}y\end{align*}
Example A
Graph the solutions to the equation \begin{align*}y=2x+5\end{align*}
Solution:
The equation is in slopeintercept form. To graph the solutions to this equation, you should start at the \begin{align*}y\end{align*}
Example B
Graph the equation \begin{align*}y=3x+5\end{align*}
Solution:
Using the definition of slopeintercept form, this equation has a \begin{align*}y\end{align*}
Slopes of Parallel Lines
Parallel lines will never intersect, or cross. The only way for two lines never to cross is if the method of finding additional coordinates is the same.
Therefore, it's true that parallel lines have the same slope.
You will use this fact in later algebra lessons as well as in geometry.
Example C
Determine the slope of any line parallel to \begin{align*}y=3x+5\end{align*}
Solution:
Because parallel lines have the same slope, the slope of any line parallel to \begin{align*}y=3x+5\end{align*}
Guided Practice
Graph \begin{align*}y=\frac{2}{5}x\end{align*}
Solution:
First, graph the \begin{align*}y\end{align*}
Next, the slope is \begin{align*}\frac{2}{5}\end{align*}
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)
Plot the following functions on a graph.

\begin{align*}y=2x+5\end{align*}
y=2x+5 
\begin{align*}y=0.2x+7\end{align*}
y=−0.2x+7 
\begin{align*}y=x\end{align*}
y=−x 
\begin{align*}y=3.75\end{align*}
y=3.75 
\begin{align*}\frac{2}{7} x4=y\end{align*}
27x−4=y 
\begin{align*}y=4x+13\end{align*}
y=−4x+13 
\begin{align*}2+\frac{3}{8} x=y\end{align*}
−2+38x=y 
\begin{align*}y=\frac{1}{2}+2x\end{align*}
y=12+2x
In 9 – 16, state the slope of a line parallel to the line given.

\begin{align*}y=2x+5\end{align*}
y=2x+5 
\begin{align*}y=0.2x+7\end{align*}
y=−0.2x+7 
\begin{align*}y=x\end{align*}
y=−x 
\begin{align*}y=3.75\end{align*}
y=3.75 
\begin{align*}y=\frac{1}{5}x11\end{align*}
y=−15x−11 
\begin{align*}y=5x+5\end{align*}
y=−5x+5 
\begin{align*}y=3x+11\end{align*}
y=−3x+11 
\begin{align*}y=3x+3.5\end{align*}
y=3x+3.5
Mixed Review
 Graph \begin{align*}x = 4\end{align*}
x=4 on a Cartesian plane.  Solve for \begin{align*}g: 811+4g=99\end{align*}
g:8−11+4g=99 .  What is the order of operations? When is the order of operations used?
 Give an example of a negative irrational number.
 Give an example of a positive rational number.
 True or false: An integer will always be considered a rational number.
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Cartesian Plane
The Cartesian plane is a grid formed by a horizontal number line and a vertical number line that cross at the (0, 0) point, called the origin.linear equation
A linear equation is an equation between two variables that produces a straight line when graphed.Linear Function
A linear function is a relation between two variables that produces a straight line when graphed.SlopeIntercept Form
The slopeintercept form of a line is where is the slope and is the intercept.Image Attributions
Here you'll learn how to use the slopeintercept form of a line to graph it, as well as how to recognize the slope of parallel lines.