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 (4,320) 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 (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)

Answer 1

To determine which two points on a linear graph indicate a rate of change of 80 km per hour, we can use the formula for the slope (rate of change) between two points \((x_1, y_1)\) and \((x_2, y_2)\):

\[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \]

For a rate of change of 80 km/h, we want:

\[ \frac{y_2 - y_1}{x_2 - x_1} = 80 \]

Now we can evaluate each pair of points:

1. (4, 320) and (6, 480):

   • \(y_2 - y_1 = 480 - 320 = 160\)
   • \(x_2 - x_1 = 6 - 4 = 2\)
   • Slope = \( \frac{160}{2} = 80 \)

2. (4, 400) and (6, 480):

   • \(y_2 - y_1 = 480 - 400 = 80\)
   • \(x_2 - x_1 = 6 - 4 = 2\)
   • Slope = \( \frac{80}{2} = 40 \)

3. (5, 400) and (6, 560):

   • \(y_2 - y_1 = 560 - 400 = 160\)
   • \(x_2 - x_1 = 6 - 5 = 1\)
   • Slope = \( \frac{160}{1} = 160 \)

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

   • \(y_2 - y_1 = 600 - 480 = 120\)
   • \(x_2 - x_1 = 6 - 4 = 2\)
   • Slope = \( \frac{120}{2} = 60 \)

From our calculations, the pair of points that gives a rate of change of 80 km/h is (4, 320) and (6, 480).