Graphing Horizontal Lines
A linear equation in two variables is an equation that can be written in the
form Ax + By = C, where A, B, and C are real numbers and A and B are
not both 0.
If either A or B is 0, the equation can be written with only one variable.
For example, the equation y = -2 is a linear equation since it can be
written as 0x + 1y = -2.
Here, A is 0, B is 1, and C is -2.
Now we will graph the equation y = -2.
Example 1
Graph y = -2.
Solution
Step 1 Make a table of ordered pairs that satisfy the equation.
Each ordered pair (x, y) that satisfies the equation
y = -2 has y-coordinate -2.
So, in the table, y is always -2.
The variable x does not appear
in the equation y = -2.
So we can let x be any real
number; but y is always -2.
|
|
x |
y |
|
-5 |
-2 |
|
-3 |
-2 |
|
0 |
-2 |
|
3 |
-2 |
|
Step 2 Plot the ordered pairs.
The points are plotted.
Step 3 Draw a line through the plotted points.
Since the y-value of each ordered pair is -2, the graph is a horizontal
line two units below the x-axis.
Every point on this line represents a solution of y = -2.
Definition —
Graph of a Horizontal Line y = k
|
The graph of an equation of the
form y = k is a horizontal line
through the point (0, k), where k
is a constant. |
 |
|
