Question

The table represents a linear function. The rate of change between the points (–5, 10) and (–4, 5) is –5. What is the rate of change between the points (–3, 0) and (–2, –5)?

x
y
–5
10
–4
5
–3
0
–2
–5
–5
Negative StartFraction 1 Over 5 EndFraction
One-fifth
5

Answer 1

The rate of change (also known as the slope) between two points \((x_1, y_1)\) and \((x_2, y_2)\) can be calculated using the formula:

\[
\text{Rate of Change} = \frac{y_2 - y_1}{x_2 - x_1}
\]

Let's calculate the rate of change between the points \((-3, 0)\) and \((-2, -5)\).

1. Identify the coordinates:
- \((x_1, y_1) = (-3, 0)\)
- \((x_2, y_2) = (-2, -5)\)

2. Plug in the values into the formula:

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

Thus, the rate of change between the points \((-3, 0)\) and \((-2, -5)\) is \(-5\).