SECTION 3.2 Graphing Linear Equations in Two Variables^193
The equation of the x-axis is the horizontal line ,and the equation of the
y-axis is the vertical line x 0.
y 0
Vertical LineThe graph of the linear equation where kis a real number, is the vertical
line with x-intercept. There is no y-intercept (unless the vertical line is the
y-axis itself ).
1 k, 0 2
xk,
CAUTION The equations of horizontal and vertical lines are often confused
with each other. Remember that the graph of is parallel to the x-axis and the
graph of x= kis parallel to the y-axis (for kZ 0 ).
y=k
A summary of the forms of linear equations from this section follows.
Graphing a Linear EquationEquation To Graph Example
Draw a horizontal line, through
Draw a vertical line, through
The graph passes through
To find additional points that lie
on the graph, choose any value
for xor y, except 0.
Find any two points on the line.
(but not of A good choice is to find the
the types intercepts. Let and find the
above) corresponding value of y. Then let
and find x.
As a check, get a third point by
choosing a value for xor ythat
has not yet been used.
y=0,
x=0,
AxByC
AxBy 0 1 0, 0 2.
1 k, 0 2.
xk
1 0, k 2.
yk
xy0
x = 4x = 2yxy0xy0
3 x – 2y = 6(2, 0)(4, 3)(0, –3)xy0
y = –2