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The table below shows \( y \), the distance an athlete runs during \( x \) seconds.

\[
\begin{array}{|c|c|}
\hline
\text{Time } (x \text{ seconds}) & \text{Distance } (y \text{ meters}) \\
\hline
50 & 7.5 \\
100 & 15.0 \\
150 & 22.5 \\
200 & 30.0 \\
250 & 37.5 \\
\hline
\end{array}
\]

The pairs of values in the table form points on the graph of a linear function. What is the approximate slope of the graph of that function?

Answer :

The approximate slope of the graph of the linear function is 0.15.

To find the approximate slope of the graph of the linear function, we can choose two points from the table and calculate the slope using the formula:

slope = (change in y) / (change in x)

Let's select the points (50, 7.5) and (250, 37.5) from the table.

Change in y = 37.5 - 7.5 = 30

Change in x = 250 - 50 = 200

slope = (change in y) / (change in x) = 30 / 200 = 0.15

Note: A linear function is a mathematical function that represents a straight line.

It can be written in the form:

f(x) = mx + b

where m is the slope of the line and b is the y-intercept (the point where the line intersects the y-axis).

The slope (m) determines the steepness or slant of the line.

A positive slope indicates an upward-sloping line, while a negative slope indicates a downward-sloping line.

The slope represents the rate of change of the function.

For similar question on linear function.

https://brainly.com/question/390660

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