Math 154 — Rodriguez
Angel — 4.2
Graphing Linear Equations
I. Graphing Linear Equations by Plotting Points
A. In the previous section we learned how to find the missing coordinate of an ordered
pair.
B. In this section we aren’t given a ‘starting value’—we get to decide what values to use.
Example 1: Find some solutions to y = –x+2.
x
y
Example 2: Find some solutions to 3x – 4y=12.
x
y
C. Graph by plotting points.
Steps:
1. Choose a value for x or y. Plug it into the equation and solve for the other
variable. (See section B above.) Write down the ordered pair (x,y).
2. Repeat step 1 with different values. You need at least 3 ordered pairs.
3. Plot the ordered pairs.
4. If the points appear collinear, draw a line with arrowheads through them. If they
do not appear collinear, check your work.
Examples: Graph by plotting points. Plot at least three points for each graph.
3) y = 3x — 2
4) 2x — 3y = 6
II. Graphing Linear Equations by Using Intercepts
A. It is easier to find and plot certain values. In particular, it is easy to find the missing
coordinate, if one of the values we choose is 0. The points we get by letting x=0 and
y=0 are ‘special’. They are called intercepts.
The x-intercept is the point where the graph intersects the x-axis.
(
The y-intercept is the point where the graph intersects the y-axis.
(
,
,
)
)
y
x
B. Graph by using intercepts.
The steps are the same as graphing by plotting points EXCEPT we are choosing to find
points where x=0 and y=0.
Steps:
1. Find the x-intercept by letting y = 0 and solving for x.
2. Find the y-intercept by letting x = 0 and solving for y.
3. Find a third point to serve as a check point. Choose any value except x=0 or
y=0.
4. Plot the ordered pairs.
5. If the points appear collinear, draw a line through them. If they do not appear
collinear, check your work. Make sure your line has arrowheads at the ends.
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Examples: Graph using the x- and y-intercepts. The graph must include 3 points.
5. y = —3x + 6
6. 6x — 12y = 18
7. —8x + 4y = 16
8.
y = 4x— 2
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III. Graphing Horizontal and Vertical Lines
A. You will notice some equations have only one variable. What do the graphs of those
equations look like?
B. Consider the equation, x = 2.
a. What ordered pairs are solutions to this equation?
b. Plot those points and draw a line through them.
c. What does the line look like?
We can generalize and say:
The graph of x = # is a _________________ line going through the point (
,
).
,
).
Likewise, any___________________ line has as its equation x = #.
Examples: Graph x = 4.
Write the equation for the given graph.
y
x
C. The graph of y = # is a ________________ line going through the point (
And any ___________________ line has as its equation y = #.
Examples: Graph y = -3.
Write the equation for the given graph.
y
x
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