GRAPHING LINEAR EQUATIONS IN TWO VARIABLES
The graphs of linear equations in two variables are straight lines. Linear equations may be written in
several forms:
Slope-Intercept Form: y = mx+ b
In an equation of the form y = mx + b, such as y = −2x − 3, the slope is m and the y-intercept is the
point (0, b). To graph equations of this form, construct a table of values (Method 1) or use the slope
and y-intercept (Method 3) (see Examples 1 and 6).
General Form: ax + by = c
To graph equations of this form, such as 3x − 2y = −6, find the x- and y-intercepts (Method 2), or solve
the equation for y to write it in the form y = mx + b and construct a table of values (see Example 2).
Horizontal Lines: y = b
The graph of y = b is a horizontal line passing through the point (0, b) on the y-axis. To graph an equation
of this form, such as y = 4, plot the point (0, b) on the y-axis and draw a horizontal line through it (see
Example 4). If the equation is not in the form y = b, solve the equation for y.
Vertical Lines: x = a
The graph of x = a is a vertical line passing through the point (a, 0) on the x-axis. To graph a vertical
line, such as 4x + 12 = 0, solve the equation for x to write it in the form x = a, plot the point (a, 0) on the
x-axis, and draw a vertical line through it (see Example 5).
METHOD 1: CONSTRUCT A TABLE OF VALUES
To graph equations of the form y = mx and y = mx + b,
1) Choose three values for x. Substitute these values in the equation and solve to find the
corresponding y-coordinates.
2) Plot the ordered pairs found in step 1.
3) Draw a straight line through the plotted points. If the points do not line up, a mistake has been made.
Example 1: Graph y = −2x − 3
To graph the equation, choose three values for x and list them in a table. (
Hint: choose values that are
easy to calculate, like −1, 0, and 1.) Substitute each value in the equation and simplify to find the
corresponding y-coordinate. Plot the ordered pairs and draw a straight line through the points.
X
Y
(- 1, - 1)
(0, -3)
(1, - 5)
x y = −2x − 3 (x, y)
−1
y = −2(−1) – 3
= 2 – 3 = −1
(−1, −1)
0 y = −2(0) – 3 = –3 (0, –3)
1
y = −2(1) – 3
= −2 – 3 = −5
(1, −5)
PBCC Page 1 of 5 SLC Lake Worth Math Lab