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

Question

Responses

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

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

(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)

Answer 1

To determine which two points indicate a rate of change of 80 km per hour, we need to find the slope between the two points, which is calculated as:

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

Where \( \Delta y \) is the change in distance and \( \Delta x \) is the change in time. In this case, we need the slope to equal 80 km/h.

1. (4, 400) and (6, 480):

   • \( \Delta y = 480 - 400 = 80 \)
   • \( \Delta x = 6 - 4 = 2 \)
   • Slope = \( \frac{80}{2} = 40 \) km/h (not 80)

2. (4, 320) and (6, 480):

   • \( \Delta y = 480 - 320 = 160 \)
   • \( \Delta x = 6 - 4 = 2 \)
   • Slope = \( \frac{160}{2} = 80 \) km/h (this is correct)

3. (4, 480) and (6, 600):

   • \( \Delta y = 600 - 480 = 120 \)
   • \( \Delta x = 6 - 4 = 2 \)
   • Slope = \( \frac{120}{2} = 60 \) km/h (not 80)

4. (5, 400) and (6, 560):

   • \( \Delta y = 560 - 400 = 160 \)
   • \( \Delta x = 6 - 5 = 1 \)
   • Slope = \( \frac{160}{1} = 160 \) km/h (not 80)

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

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