Graphs of Lines from Equations
The graph of any linear function can be plotted using the slopeintercept form of the equation.
Step 1: Solve the equation for
Step 2: To graph the function, start by plotting the
Step 3: Use the slope to find another point on the line. From the
Step 4: Connect these two points to form a line and extend the line.
Note that you can repeat Step 3 multiple times in order to find more points on the line if you wish.
Because the equations of horizontal and vertical lines are special, these types of lines can be graphed differently:
 The graph of a horizontal line will have an equation of the form
y=a wherea is the yintercept of the line. You can simply draw a horizontal line through the yintercept to sketch the graph.  The graph of a vertical line will have an equation of the form
x=c , wherex is the xintercept of the line. You can simply draw a vertical line through the xintercept to sketch the graph.
Let's practice by finding the yintercept and slope of the following function:
The first step is to rewrite the equation in the form
The
Now, let's graph the following function:
The
From the
Join the points with a straight line. Use a straight edge to draw the line.
Finally, let's plot the following linear equations on a Cartesian grid:

x=3
A line that has
y=5
A line that
Examples
Example 1
Earlier, you were asked to plot the linear function
The first step is to rewrite the function in slopeintercept form.
The slope of the line is
Plot the
Example 2
Using the slopeintercept method, graph the linear function
The slope of the line is
Example 3
Using the slopeintercept method, graph the linear function
Write the equation in slopeintercept form.
7x−3y−15=07x−7x−3y−15=0−7x 3y−15=7x3y−15+15=7x+153y=7x+15 3y3=7x3+153 y=73x−5Solve the equation for y.  The slope is
73 and they intercept is (0, 5). Plot they intercept. Apply the slope to they intercept. Use a straight edge to join the two points.
Example 4
Graph the following lines on the same Cartesian grid. What shape is formed by the combination of the graphs ad?

y=3 
x=4 y=2 x=−6
There are four lines to be graphed. The lines
Review
For each of the following linear functions, state the slope and the \begin{align*}y\end{align*}intercept:
 \begin{align*}y=\frac{5}{8}x+3\end{align*}
 \begin{align*}4x+5y3=0\end{align*}
 \begin{align*}4x3y+21=0\end{align*}
 \begin{align*}y=7\end{align*}
 \begin{align*}9y8x=27\end{align*}
Using the slopeintercept method, graph the following linear functions:
 \begin{align*}3x+y=4\end{align*}
 \begin{align*}3x2y=\text{}4\end{align*}
 \begin{align*}2x+6y+18=0\end{align*}
 \begin{align*}3x+7y=0\end{align*}
 \begin{align*}4x5y=\text{}30\end{align*}
 \begin{align*}6x2y=8\end{align*}
Graph the following linear equations and state the slope of the line:
 \begin{align*}x=\text{}5\end{align*}
 \begin{align*}y=8\end{align*}
 \begin{align*}y=\text{}4\end{align*}
 \begin{align*}x=7\end{align*}
Review (Answers)
To see the Review answers, open this PDF file and look for section 4.4.