Point-slope form
Distributive property
Add 183.
Retail spending y(in billions of dollars) on prescription drugs in the United States in
year xcan be approximated by the equation y=15.2x+ 152.6.
y=15.2x+ 152.6
y- 183 =15.2x- 30.4
y- 183 =15.2 1 x- 22 1 x 1 , y 12 = 1 2, 183 2 ; m=15.2
y-y 1 =m 1 x-x 12
SECTION 3.3 Linear Equations in Two Variables 169
3.3 EXERCISES
Complete solution available
on the Video Resources on DVD
Either point can be used
here. 7, 259 provides
the same answer.
1 2
(b)Use the equation from part (a) to estimate retail spending on prescription drugs
in the United States in 2010. (Assume a constant rate of change.)
Since represents 2002 and 2010 is 8 yr after 2002, represents 2010.
Equation from part (a)
Substitute 10 for x.
Multiply, and then add.
About $305 billion was spent on prescription drugs in 2010. NOW TRY
y= 304.6
y= 15.2 1102 +152.6
y= 15.2x+ 152.6
x= 2 x= 10
We can use a graphing calculator to solve a linear equation in one variable, such as
We must write the equation as an equivalent equation with 0 on one side.
Subtract 3xand 4.
Then we graph
to find the x-intercept. (The word “Zero” indicates that the x-intercept has been located.)
The standard viewing window cannotbe used here because the x-intercept does not lie
in the interval SeeFIGURE 35. The x-intercept of the graph is the point
. Thus, the solution of the equation is , and the solution set is
For Discussion or Writing
Use a graphing calculator to solve each equation.
1. 2.
3. 312 x+ 12 - 21 x- 22 = 5 4. 41 x- 32 - x= x- 6
7 x- 2 x+ 4 - 5 = 3 x- 1 31 x- 72 + 4 x=- 3 x- 11
1 - 12, 0 2 - 12 5 - 126.
3 - 10, 10 4.
Y=-2X - 412 - X 2 - 3X- 4
- 2 x- 412 - x 2 - 3 x- 4 = 0
- 2 x- 412 - x 2 = 3 x+4.
CONNECTIONS
10
–20
- 15 5
Y = – 2X – 4(2 – X) – 3X – 4
FIGURE 35
NOW TRY
EXERCISE 9
Refer to Example 9.
(a)Use the ordered pairs
and to
write an equation that
models the data.
(b)Use the equation from part
(a) to estimate retail
spending on prescription
drugs in 2011.
1 2, 183 2 1 6, 251 2
NOW TRY ANSWERS
- (a)
(b)$336 billion
y= 17 x+ 149
Concept Check In Exercises 1– 6, provide the appropriate response.
1.The following equations all represent the same line. Which one is in standard form as
defined in the text?
A. B. C. D.
2.Which equation is in point-slope form?
A.y= 6 x+ 2 B. 4 x+y= 9 C.y- 3 = 21 x- 12 D. 2 y= 3 x- 7
3 x= 2 y+ 5
3
5
x-
2
5
3 x- 2 y= 5 2 y= 3 x- 5 y= 1