Question

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the graph shows the distance traveled by an olympic - level sprinter over time during a race. find the slope of the line, and complete the sentences below. 100 - meter race the slope of the line is 10. the slope represents choose... choose... the distance the sprinter runs the sprinters speed in seconds per meter the sprinters speed in meters per second the time the sprinter runs

Explanation:

Step1: Recall slope formula

The slope formula for a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$. For the given graph, we can take two points, say $(0,0)$ and $(10,100)$.

Step2: Calculate the slope

Substitute $x_1 = 0,y_1=0,x_2 = 10,y_2 = 100$ into the slope formula: $m=\frac{100 - 0}{10 - 0}=\frac{100}{10}=10$.

Step3: Interpret the slope

In the context of distance - time graph, slope $m=\frac{\text{Change in distance}}{\text{Change in time}}$. Since distance is in meters and time is in seconds, the slope represents the speed of the sprinter in meters per second.

Answer:

The slope of the line is $10$. The slope represents the sprinter's speed in meters per second.