Question

Which two points on a linear graph showing time and distance would indicate a rate of change of 80 km per hour?

(4,320) and (6,480)
(4,400) and (6,480)
(5,400) and (6,560)
(4,480) and (6,600)

Answer 1

To determine which two points indicate a rate of change of 80 km per hour on a linear graph showing time and distance, we need to use the following formula for the rate of change:

\[
\text{Rate} = \frac{\text{Change in distance}}{\text{Change in time}}
\]

We are looking for a rate of 80 km/h. This means that for every hour (1 unit of time), the distance should change by 80 km.

Let's evaluate each pair of points:

1. **(4, 320) and (6, 480)**
- Change in distance: \(480 - 320 = 160\) km
- Change in time: \(6 - 4 = 2\) hours
- Rate: \(\frac{160}{2} = 80\) km/h (This works)

2. **(4, 400) and (6, 480)**
- Change in distance: \(480 - 400 = 80\) km
- Change in time: \(6 - 4 = 2\) hours
- Rate: \(\frac{80}{2} = 40\) km/h (Not 80 km/h)

3. **(5, 400) and (6, 560)**
- Change in distance: \(560 - 400 = 160\) km
- Change in time: \(6 - 5 = 1\) hour
- Rate: \(\frac{160}{1} = 160\) km/h (Not 80 km/h)

4. **(4, 480) and (6, 600)**
- Change in distance: \(600 - 480 = 120\) km
- Change in time: \(6 - 4 = 2\) hours
- Rate: \(\frac{120}{2} = 60\) km/h (Not 80 km/h)

The only pair of points that indicates a rate of change of 80 km per hour is:

**(4, 320) and (6, 480)**