Question

is the rate of change of the function 5?

a yes, because y changes by 5 every time x changes by 1.
b yes, because y changes by 1 every time x changes by 5.

Explanation:

⚡ Using what you learned: Rate of Change and Applications

Step 1: Identify points on the line

Identify two points where the line crosses the grid intersections perfectly:

• Point 1: \((0, -3)\)
• Point 2: \((1, 2)\)

Step 2: Calculate the rate of change

Use the rate of change formula:

$$ \text{Rate of Change} = \frac{\text{Change in } y}{\text{Change in } x} = \frac{y_2 - y_1}{x_2 - x_1} $$

$$ \text{Rate of Change} = \frac{2 - (-3)}{1 - 0} = \frac{5}{1} = 5 $$

This means \(y\) increases by \(5\) units for every \(1\) unit increase in \(x\).

Answer:

A Yes, because y changes by 5 every time x changes by 1.