Question

is the rate of change of the function 5?

yes, because y changes by 5 every time x changes by 1.
yes, because y changes by 1 every time x changes by 5.
no, because y does not change by 5 every time x changes by 1.
no, because y does not change by 1 every time x changes by 5.

Explanation:

Identify points on the line

Using the Slope of a Line knowledge point

$$
LATEXBLOCK0
$$

Calculate the rate of change

Using the Slope of a Line knowledge point

$$
LATEXBLOCK1
$$

Compare with the given rate

The calculated rate of change is \(4\), which is not equal to \(5\). Therefore, the rate of change of the function is not \(5\).

Analyze the options

Since the rate of change is \(4\), \(y\) changes by \(4\) units for every \(1\) unit change in \(x\). Thus, \(y\) does not change by \(5\) every time \(x\) changes by \(1\).

Answer:

• Yes, because y changes by 5 every time x changes by 1.
• Yes, because y changes by 1 every time x changes by 5.
• No, because y does not change by 5 every time x changes by 1. (Correct answer)
• No, because y does not change by 1 every time x changes by 5.