Question

Determine whether the function is linear. If it is, State the rate of change.Question 8

Answer 1

Question 8.

Given the table:

x -7 -5 -3 -1 0

y 11 14 17 20 23

To determine if the function is linear, let's calculate to see if the rate of change is constant.

The x-values need to have a constant rate of change and the y-values need to have a constant rate of change.

If the function has a constant rate of change, then the functioncan be said to be linear.

To calculate the rate of change, we have:

`\begin{gathered} x2-x1=-5\text{ - (-7) = -5 + 7 = 2} \\ \\ x3-x2=-3-(-5)=-3+5=2 \\ \\ x4-x3=-1-(-3)=-1+3=2 \\ \\ x5-x4=0-(-1)=0+1=1 \\ \\ We\text{ can se}e\text{ the x-values do not have a constant rate of change} \end{gathered}`
`\begin{gathered} y2-y1=14-11=3 \\ \\ y3-y2=17-14=3 \\ \\ y4-y3=20-17=3 \\ \\ y5-y4=23-20=3 \\ \\ \text{The y-values have a constant rate of change} \end{gathered}`

Since the x-values do not have a constant rate of change that means the function is not linear.

ANSWER:

The table does not represent a linear function