Question

Which two points on a linear graph showing time and distance would indicate a rate of change of 80km per hour
(4,400) And (6,480)
(4,480)And (6,600)
(4,320)And (6,480)
(5,400)And (6,560)

Answer 1

To determine which pair of points indicates a rate of change of 80 km per hour, we need to calculate the slope (rate of change) using the formula:

\[
\text{slope} = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1}
\]

where \( \Delta y \) is the change in distance and \( \Delta x \) is the change in time.

We will evaluate each option:

1. **(4,400) and (6,480)**:
\[
\Delta y = 480 - 400 = 80
\]
\[
\Delta x = 6 - 4 = 2
\]
\[
\text{slope} = \frac{80}{2} = 40 \text{ km/h}
\]


2. **(4,480) and (6,600)**:
\[
\Delta y = 600 - 480 = 120
\]
\[
\Delta x = 6 - 4 = 2
\]
\[
\text{slope} = \frac{120}{2} = 60 \text{ km/h}
\]

3. **(4,320) and (6,480)**:
\[
\Delta y = 480 - 320 = 160
\]
\[
\Delta x = 6 - 4 = 2
\]
\[
\text{slope} = \frac{160}{2} = 80 \text{ km/h}
\]

4. **(5,400) and (6,560)**:
\[
\Delta y = 560 - 400 = 160
\]
\[
\Delta x = 6 - 5 = 1
\]
\[
\text{slope} = \frac{160}{1} = 160 \text{ km/h}
\]

From the calculations, the pair of points **(4,320) and (6,480)** indicates a rate of change of **80 km per hour**.