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Chapter 9: Q63. (page 596)

The table shows the cost to purchase school-spirit posters. Determine which kind of model best describes the data. Then write the equation.

No. of posters

2

4

6

8

Cost

4

7

10

13

Short Answer

Expert verified

The equation of the function that models best the given data is y=32x+1.

Step by step solution

01

Step 1. Determine the rate.

From the table it can be observed that as x increases by 2, the yincreases by 3.

Therefore,

role="math" localid="1647851209614" Rate=slope=肠丑补苍驳别鈥夆赌夆赌塷蹿鈥夆赌夆赌�y肠丑补苍驳别鈥夆赌夆赌塷蹿鈥夆赌夆赌�x=32

02

Step 2. Write an equation for the functions that models the data.

Since the rate is constant; the table of values represents a linear function of the formy=ax+b . Since the rate is 32, so a=32.

03

Step 3. Simplify the equation for the function.

To find b, use an ordered pair from the table, such as (2,4).

role="math" localid="1647851305451" y=ax+b4=32(2)+b鈥夆赌夆赌夆赌夆赌夆赌夆赌夆赌�[x=2,y=4]4=3+bb=1y=32x+1

Therefore, the equation that models the data is y=32x+1.

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