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

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

1 answer

To determine which two points indicate a rate of change of 80 km per hour, we can use the formula for the rate of change between two points \((t_1, d_1)\) and \((t_2, d_2)\):

\[ \text{Rate of change} = \frac{d_2 - d_1}{t_2 - t_1} \]

We need the rate of change to be 80 km/h. Let's calculate the rate of change for each pair of points provided.

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

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

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

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

From these calculations, the only pair of points that gives a rate of change of 80 km per hour is:

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