Question

amara always charges the battery of her motorized wheelchair overnight. at the end of each day, she records the distance she traveled and the remaining charge on the battery. the scatter plot shows the data.

the equation of the line of fit is $y = -3.8x + 100$.
what is the slope of the line and what does it mean?
the slope is ? . an increase of ? in the distance traveled ? the remaining charge by ? .

Explanation:

Step1: Identify the slope

The line is given in slope-intercept form $y = mx + b$, where $m$ is the slope. For $y = -3.8x + 100$, the slope $m = -3.8$.

Step2: Interpret slope variables

Here, $x$ = distance traveled (miles), $y$ = remaining charge (%). Slope = $\frac{\text{Change in } y}{\text{Change in } x}$.

Step3: Explain slope meaning

A slope of $-3.8$ means for each 1-unit increase in $x$ (distance), $y$ (remaining charge) decreases by 3.8.

Answer:

The slope is $\boldsymbol{-3.8}$. An increase of $\boldsymbol{1}$ mile in the distance traveled $\boldsymbol{decreases}$ the remaining charge by $\boldsymbol{3.8}$ percentage points.