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Chapter 9: Q62. (page 596)

Look for a pattern in each table of values to determine which kind of model best describes the data. Then write an equation for the function that models the data.

x

0

1

2

3

4

y

3

6

9

12

15

Short Answer

Expert verified

The equation of the function that models best the given data is y=3x+3.

Step by step solution

01

Step 1. Determine the rate.

For x=0and y=3, this means y鈥搃ntercept is 3. Note that as xincreases by 1, the yincreases by 3. Therefore,

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=31=3

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 form y=ax+b. Since the rate is 3, so b=3.

03

Step 3. Simplify the equation for the function.

To find a, use an ordered pair from the table, such as (1,6).

role="math" localid="1647850952463" y=ax+b6=a(1)+3鈥夆赌夆赌夆赌夆赌夆赌夆赌夆赌�[x=1,y=6]6鈭�3=aa=3y=3x+3

Therefore, the equation that models the data is y=3x+3.

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