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

(4,480)
and (6,600)
left parenthesis 4 comma 480 right parenthesis and left parenthesis 6 comma 600 right parenthesis

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

(4,400)
and (6,480)
left parenthesis 4 comma 400 right parenthesis and left parenthesis 6 comma 480 right parenthesis
Remaining Attempts : 3

Answer 1

To determine which two points on a linear graph indicate a rate of change of 80 km per hour, we first need to understand that the rate of change (slope) can be calculated using the formula:

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

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

Let's calculate the slope for each pair of points:

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

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

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

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

From the calculations above, the pair of points **(4, 320) and (6, 480)** gives a slope of 80 km/h.

So the correct response is:
**(4, 320) and (6, 480)**.