Section 23
Graphing Linear Equations
If you have two points, you can draw a straight line connecting them.
So, if you have an equation in two variables and you know that equation is
linear (which means its graph is a line), it’s easy to graph it. All
you need to do is find two
ordered pair
solutions, plot them, and then draw
the line connecting them. (It’s a good idea to do a third point to check
yourself.)
Example:
Graph the equation
y
= 2
x
+ 3
.
Start by choosing some easy points for
x
, (say 0, 1, and 2), plug
them in, and calculate the corresponding
y
values.
x

y

0

2(0) + 3 = 3

1

2(1) + 3 = 5

2

2(2) + 3 = 7

Now, plot the points (0, 3), (1, 5), and (2, 7), and draw the line connecting
them.
Easy!
Sometimes, things can be a little more complicated if the original equation
does not have
y
alone on one side. In this case, you have to solve
for
y
first, and then get your ordered pairs.
Example:
Graph the equation
3
y
+ 1 = –4
x
+ 2
y
.
Start by collecting like terms on one side. Subtract 2
y
from both
sides.
y
+ 1 = –4
x
Then subtract 1 from both sides.
y
= –4
x
– 1
Now you can plug in some values of
x
and quickly get the corresponding
y
values.
HORIZONTAL AND VERTICAL LINES
Equations of
horizontal and vertical lines
only have one variable. The equation
x
= 4
represents a vertical line which crosses the
x
axis at the point
(4, 0). Every ordered pair with 4 as its first coordinate is a solution. (The
equation means “
x
is equal to 4, and
y
can be whatever
it wants.”)
Similarly, the equation
y
= –3
is a horizontal line which crosses the
y
axis at (0,
–
3).
The point where the horizontal and vertical lines intersect is also easy
to find.