Question

eliot collected the air temperature and the water temperature at a local river for seven days. his data is displayed on the scatter plot. the equation of the line of best fit is y = 0.5x + 25, where x is the air temperature and y is the water temperature. what is the meaning of the slope of the line of best fit? a. the water temperature is expected to be 0.5 °f less than the air temperature. b. the water temperature is expected to be 0.5 °f greater than the air temperature. c. when the air temperature increases by 1 °f, the water temperature is expected to decrease by 0.5 °f. d. when the air temperature increases by 1 °f, the water temperature is expected to increase by 0.5 °f.

Explanation:

In a linear equation $y = mx + b$ (here $y = 0.5x+25$), the slope $m$ represents the change in $y$ for a unit - change in $x$. When $x$ (air temperature) increases by $1^{\circ}F$, $y$ (water temperature) changes by the value of the slope. Since the slope $m = 0.5$, when the air temperature increases by $1^{\circ}F$, the water temperature is expected to increase by $0.5^{\circ}F$.

Answer:

D. When the air temperature increases by 1°F, the water temperature is expected to increase by 0.5°F