Question

7 evan performed an experiment testing how different wind speeds affect how fast a small cart will roll down a ramp. his data from the experiment is shown in the graph below. time (s) vs. wind speed (m/s) which of the following equations is a best fit for the data? 9s + 5 0.65s + 5 -5s - 9 -0.25s + 9

Explanation:

Step1: Analyze the slope of the data trend

The data points show a decreasing trend as wind speed ($s$) increases. So the slope of the linear equation should be negative.

• For the equation $9s + 5$, the slope $m = 9>0$.
• For the equation $0.65s + 5$, the slope $m=0.65>0$.
• For the equation $-5s - 9$, when $s = 0$, $y=-9$ which is not in line with the graph (when $s = 0$, $y\approx9.5$).
• For the equation $- 0.25s+9$, the slope $m=-0.25<0$.

Step2: Analyze the y - intercept

When $s = 0$, from the graph, the time (y - value) is close to $9.5$.

• For $-0.25s + 9$, when $s = 0$, $y = 9$ which is relatively close to the value at $s = 0$ in the graph compared to $-5s-9$ (where $y=-9$ when $s = 0$).

Answer:

$-0.25s + 9$