4.4: Graphs of Lines from Equations
Can you graph the linear function
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Khan Academy Slope and yIntercept Intuition
Guidance
The graph of any linear function can be plotted using the slopeintercept form of the equation.
 Step 1: Solve the equation for
y if it is not already in the formy=mx+b .  Step 2: To graph the function, start by plotting the
y intercept.  Step 3: Use the slope to find another point on the line. From the
y intercept, move to the right the number of units equal to the denominator of the slope and then up or down the number of units equal to the numerator of the slope. Plot the point.  Step 4: Connect these two points to form a line and extend the line.
Note: 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.
Example A
For the following linear function, state the
Solution:
The first step is to rewrite the equation in the form
The
Example B
Graph the linear function
Solution:
The
From the
Join the points with a straight line. Use a straight edge to draw the line.
Example C
Plot the following linear equations on a Cartesian grid.
i)
ii)
Solution:
i) A line that has
ii) A line that
Concept Problem Revisited
Plot the linear function
The first step is to rewrite the function in slopeintercept form.
The slope of the line is
Plot the
Vocabulary
 SlopeIntercept Form
The slopeintercept form is one method for writing the equation of a line. The slopeintercept form is
Guided Practice
1. Using the slopeintercept method, graph the linear function
2. Using the slopeintercept method, graph the linear function
3. Graph the following lines on the same Cartesian grid. What shape is formed by the graphs?

(a)
y=−3 
(b)
x=4 
(c)
y=2 
(d)
x=−6
Answers:
1. The slope of the line is
2. Write the equation in slopeintercept form.

7x−3y−15=07x−7x−3y−15=0−7x −3y−15=−7x−3y−15+15=−7x+15−3y=−7x+15 −3y−3=−7x−3+15−3 y=73x−5Solve the equation in terms of the variable y.  The slope is \begin{align*}\frac{7}{3}\end{align*} and the \begin{align*}y\end{align*}intercept is (0, 5). Plot the \begin{align*}y\end{align*}intercept. Apply the slope to the \begin{align*}y\end{align*}intercept. Use a straight edge to join the two points.
3. There are four lines to be graphed. The lines \begin{align*}a\end{align*} and \begin{align*}c\end{align*} are lines with a slope of zero and are parallel to the \begin{align*}x\end{align*}axis. The lines \begin{align*}b\end{align*} and \begin{align*}d\end{align*} are lines that have a slope that is undefined and are parallel to the \begin{align*}x\end{align*}axis. The shape is a rectangle.
Practice
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=4\end{align*}
 \begin{align*}2x+6y+18=0\end{align*}
 \begin{align*}3x+7y=0\end{align*}
 \begin{align*}4x5y=30\end{align*}
Graph the following linear equations and state the slope of the line:
 \begin{align*}x=5\end{align*}
 \begin{align*}y=8\end{align*}
 \begin{align*}y=4\end{align*}
 \begin{align*}x=7\end{align*}
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Here you will learn how to graph a linear function from its equation without first making a table of values.
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