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Chapter 9: Q28. (page 597)

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.

x01234
y13579

Short Answer

Expert verified

The equation of the function that models best the given data is y=2x+1.

Step by step solution

01

Step 1. Determine the rate.

For x=0and y=1, this means y-intercept is 1. Note that as x increases by 1, the y increases by 2. 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=21=2

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 2, so a=2.

03

Step 3. Simplify the equation for the function.

To find b, use an ordered pair from the table, such as (1, 3).

y=ax+b3=21+b鈥夆赌夆赌夆赌夆赌夆赌夆赌夆赌�[x=1,y=3]3鈭�2=bb=1y=2x+1

Therefore, the equation that models the data is y=2x+1.

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