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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) Respon...Asked by woosan♥
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 (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 (4,400) and (6,480)
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Answered by
GPT-4o mini
To determine which two points indicate a rate of change of 80 km per hour, we need to calculate the slope (rate of change) between pairs of points on the graph. The formula for the slope (rate of change) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:
\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}
\]
In this case, we want the slope to equal 80 km/hr.
Let's analyze the provided points:
1. **Points (4, 320) and (6, 480)**:
\[
\text{slope} = \frac{480 - 320}{6 - 4} = \frac{160}{2} = 80
\]
2. **Points (5, 400) and (6, 560)**:
\[
\text{slope} = \frac{560 - 400}{6 - 5} = \frac{160}{1} = 160 \text{ (not 80)}
\]
3. **Points (4, 480) and (6, 600)**:
\[
\text{slope} = \frac{600 - 480}{6 - 4} = \frac{120}{2} = 60 \text{ (not 80)}
\]
4. **Points (4, 400) and (6, 480)**:
\[
\text{slope} = \frac{480 - 400}{6 - 4} = \frac{80}{2} = 40 \text{ (not 80)}
\]
From the calculations, the only pair of points that indicates a rate of change of 80 km per hour is:
**(4, 320) and (6, 480)**.
\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}
\]
In this case, we want the slope to equal 80 km/hr.
Let's analyze the provided points:
1. **Points (4, 320) and (6, 480)**:
\[
\text{slope} = \frac{480 - 320}{6 - 4} = \frac{160}{2} = 80
\]
2. **Points (5, 400) and (6, 560)**:
\[
\text{slope} = \frac{560 - 400}{6 - 5} = \frac{160}{1} = 160 \text{ (not 80)}
\]
3. **Points (4, 480) and (6, 600)**:
\[
\text{slope} = \frac{600 - 480}{6 - 4} = \frac{120}{2} = 60 \text{ (not 80)}
\]
4. **Points (4, 400) and (6, 480)**:
\[
\text{slope} = \frac{480 - 400}{6 - 4} = \frac{80}{2} = 40 \text{ (not 80)}
\]
From the calculations, the only pair of points that indicates a rate of change of 80 km per hour is:
**(4, 320) and (6, 480)**.
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