Question

determining a linear relationship

the scatterplot shows a linear relationship between the distance traveled and the time elapsed. what is the rate of change of the linear relationship?

for every increase in time by 1 hour, the distance increases

36 miles.
54 miles.
72 miles.
90 miles.

Explanation:

Identify given coordinates

Using the Slope Formula knowledge point

$$ (x_1, y_1) = (0.25, 18),\quad (x_2, y_2) = (0.75, 54) $$

Calculate rate of change

Using the Slope Formula knowledge point

$$ m = \frac{54 - 18}{0.75 - 0.25} = \frac{36}{0.5} = 72 $$

Interpret rate of change

Using the Rate of Change Interpretation knowledge point

$$ \text{Rate} = 72\text{ miles per hour} $$

Answer:

• 36 miles.
• 54 miles.
• 72 miles. (Correct answer)
• 90 miles.