Question

Which two points on a linear graph showing time and distance would indicate a rate of change of 80 km per hour?(1 point)
Responses

(4, 480) and (6, 600)
(4, 480) and (6, 600)

(5, 400) and (6, 560)
(5, 400) and (6, 560)

(4, 400) and (6, 480)
(4, 400) and (6, 480)

(4, 320) and (6, 480)

Answer 1

To determine which two points indicate a rate of change of 80 km per hour on a linear graph of time and distance, you can use the formula for the rate of change (slope):

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

The points on the graph are given in the form (time, distance). Let's examine each pair of points to find the one that yields a rate of 80 km/h.

1. **(4, 480) and (6, 600)**:
- Change in distance: 600 - 480 = 120 km
- Change in time: 6 - 4 = 2 hours
- Rate = 120 km / 2 hours = 60 km/h

2. **(5, 400) and (6, 560)**:
- Change in distance: 560 - 400 = 160 km
- Change in time: 6 - 5 = 1 hour
- Rate = 160 km / 1 hour = 160 km/h

3. **(4, 400) and (6, 480)**:
- Change in distance: 480 - 400 = 80 km
- Change in time: 6 - 4 = 2 hours
- Rate = 80 km / 2 hours = 40 km/h

4. **(4, 320) and (6, 480)**:
- Change in distance: 480 - 320 = 160 km
- Change in time: 6 - 4 = 2 hours
- Rate = 160 km / 2 hours = 80 km/h

Thus, the correct pair of points that indicates a rate of change of 80 km per hour is:

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