Chapter 8.6, Problem 25E

To determine

To show:

The given table represents a linear function. Then write an equation for the function.

Answer to Problem 25E

The table represents a linear function. Our required equation would be $y=\frac{1}{2}x-3$ .

Explanation of Solution

Given:

A table:

  

Calculation:

To show whether our given table represents a linear function or not, we will see if the values in table has a constant rate of change.

We can see from our table that as x increases by 2 units, y increases by 1 unit.

  

So our given table has a constant rate of change that is equal to $\frac{1}{2}$ . Therefore, the given table represents a linear function.

The slope of line is $\frac{1}{2}$ . We can see from our given tables that the value of y -intercept is $-3$ .

Therefore, our required equation would be $y=\frac{1}{2}x-3$ .