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Graphing Linear Equations and Inequalities
5.2.3 Graphs of Equations in the form Ax +By =C
Steps to graph a linear equation in the form Ax +By =C
To graph a linear equation in the form Ax + By = C:
1. Solve
Ax + By = C for y. That is, isolate y to get the equation in
the form y = mx + b.
2. Graph by plotting three points.
i. Pick three values for x.
ii. For each x chosen in step i, use the equation from step i
( y = mx + b) to compute the three corresponding values of y .
iii. Plot the three ordered pairs and use a ruler to draw a line
through the points. Draw the line through the entire grid and
draw arrowheads at each end of the line to show that the line
continues indefinitely.
Example 10 Graph 2x + 3y = 6 by finding three solutions.
1. Solve the equation for y.
2. Compute three points and graph.

3. Write the orderedpair where the
graph intersects the xaxis.
4. Write the orderedpair where the graph intersects the yaxis.
Example 11 Graph 2x  5y =10 by finding three
solutions.
1. Solve the equation for y.
2. Compute three points and graph.

3. The xintercept in a graph is the orderedpair
(x, y) location
where the graph intersects the xaxis.
Write the x intercept in the graph of 2x  5y =10.
What is the value of the ycomponent of the xintercept?
4. The yintercept in a graph is the orderedpair (x, y) location
where the graph intersects the yaxis.
Write the yintercept in the graph of 2x  5y =10.
What is the value of the xcomponent of the yintercept?
5.2.4 Graph lines using the x and yIntercepts
Intercepts of a Curve (Graph)
The xintercept of a graph is the point (ordered pair location) where
the graph intersects the xaxis. The yintercept of a graph is the
ordered pair location where the graph intersects the yaxis.
Example 5
a. Identify the intercepts of each curve.
b. What is the y value of all xintercepts? 
Finding intercepts when given an equation.
1. All xintercepts are in the form (a, 0), where a is a constant
[ number ]. To find the xintercept, set y = 0 and solve for x.
2. All yintercepts are in the form (0, a), where a is a constant. To
find the yintercept, set x = 0 and solve for y.
Example 12
Find the x and yintercepts in the graph of
5x + 4y = 20. Then graph the line.
Solution
An xintercept is in the form (?, 0). Thus, set y = 0 and find the
corresponding value of x.
A yintercept is in the form (0, ?). Thus, set x = 0 and
find the
corresponding value of y.
Thus, the xintercept is (4, 0) and the yintercept is (0, 5). Now, graph the line using the intercepts. 
Example 13 Find the x and yintercepts of 3x + 7y
= 21 and
graph the line.
Example 15 Find the x and yintercepts of 3x  4y
=12 and graph
the line.
Mentally finding an xintercept
Recall, an xintercept is in the form (___, 0). So, to find the xintercept
set y = 0 and solve for the x coordinate . Then write the
intercept as an orderedpair. Since setting y = 0 makes the term
containing y disappear, you can simply cover the “yterm” and
mentally solve for x. In the following illustration, the shadedout
parts indicate the computations done mentally:
Conventional method of finding the x intercept 
Mentally find the xintercept 

x  int . is (2,0) 
Since y = 0, the term containing y disappears. So, just put your finger over the y term and mentally solve –4x = 8 to get x = 2. 

Thus the xintercept is (2, 0). Similarly, covering the
xterm will
allow you to mentally find that the yintercept is (0, 8).
Example 16
Find the x and yintercepts in the graph of each equation.
Equation Ax + By = C 
A  B  C  xintercept (a, 0) 
yintercept (0, b) 
Equations & Graphs of Horizontal and Vertical Lines
Horizontal Lines All horizontal lines have the equation y = b, where b is a constant. The yintercept in the graph of y = b is (0, b). 

Vertical Lines All vertical lines have the equation x = a, where a is a constant. The xintercept in the graph of x = a is (a, 0). 

Example 18 Graph each equation. Label each graph. a. x = 5 b. y = 7 c. x = 3 d. y = 1 e. What is the equation of line lying on the xaxis? f. What is the equation of the line lying on the yaxis? 
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