SECTION 3.2 Graphing Linear Equations in Two Variables^195
7.Concept Check Match the information about each graph in Column I with the correct
linear equation in Column II.
I
(a)The graph of the equation has y-intercept
(b)The graph of the equation has as x-intercept and
y-intercept.
(c) The graph of the equation does not have an x-intercept.
(d)The graph of the equation has x-intercept. 1 4, 0 21 0, 0 2
1 0, - 42.
8.Concept Check Which of these equations have a graph with only one intercept?
A.x+ 8 = 0 B. x-y= 3 C.x+y= 0 D.y= 4Among the basic features of graphing calculators is their ability to graph equa-
tions. We must solve the equation for yin order to enter it into the calculator. Also,
we must select a “window” for the graph, determined by the minimum and maximum
values of xand y. The standard windowis from to and from
to written with the x-interval first.
To graph discussed in Example 3,we first solve for y.
Subtract 2x.We enter this equation into the calculator and choose the standard window to get the
graph in FIGURE 16. The line intersects the x-axis at indicating that 2 is the
solution of the equation
For Discussion or Writing
Rewrite each equation with the left side equal to 0, the form required for a graph-
ing calculator. (It is not necessary to clear parentheses or combine like terms.)
1. 3 x+ 4 - 2 x- 7 = 4 x+ 3 2. 5 x- 15 = 31 x- 22
- 2 x+ 4 = 0.
1 2, 0 2 ,
y=- 2 x+ 4
2 x+y= 4,
y=- 10 y=10, 3 - 10, 10 4 , 3 - 10, 10 4 ,
x=- 10 x= 10
CONNECTIONS
10- 10
- 10 10
FIGURE 16Complete solution available
on the Video Resources on DVD
3.2 EXERCISES
Use the given equation to complete the given ordered pairs. Then graph each equation by
plotting the points and drawing a line through them. See Examples 1 and 2.
- 1 0, 2 , 1 , 0 2 , 1 5, 2
x-y= 2
1 0, 2 , 1 , 0 2 , 1 2, 2x+y= 53. 4.
1 0, 2 , 1 4, 2 , 1 - 4, 2
y=-3
4
x+ 21 0, 2 , 1 3, 2 , 1 - 3, 2
y=2
3
x+ 15. 6.
1 , 0 2 , 1 0, 2 , a ,
1
2
bx= 2 y+ 31 0, 2 , 1 , 0 2 , a-
1
3
, b
3 x=-y- 6II
A.
B.
C.
D. y= 4y= 4 xx- 4 = 03 x+y=- 4