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

(5,400)
(
5
,
400
)
and (6,560)
(
6
,
560
)
left parenthesis 5 comma 400 right parenthesis and left parenthesis 6 comma 560 right parenthesis

(4,320)
(
4
,
320
)
and (6,480)
(
6
,
480
)
left parenthesis 4 comma 320 right parenthesis and left parenthesis 6 comma 480 right parenthesis

(4,400)
(
4
,
400
)
and (6,480)
(
6
,
480
)
left parenthesis 4 comma 400 right parenthesis and left parenthesis 6 comma 480 right parenthesis

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

Answer 1

To determine which two points indicate a rate of change of 80 km per hour, we can use the formula for the slope of a line, which is:

\[
\text{slope} = \frac{\text{change in distance}}{\text{change in time}}
\]

In this case, we want the slope to equal 80 km/h. This means:

\[
80 = \frac{\Delta \text{distance}}{\Delta \text{time}}
\]

Rearranging gives us:

\[
\Delta \text{distance} = 80 \times \Delta \text{time}
\]

Now, let's analyze the choices in terms of changes in distance and time.

**Choice 1:** Points (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)

**Choice 2:** Points (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 is 80 km/h)

**Choice 3:** Points (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)

**Choice 4:** Points (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)

From the analysis, the only pair that results in a rate of change of 80 km per hour is:

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