Question

How can a linear equation model the number of calories you burn exercising?

Include the following in your answer:

• A scatter plot and a prediction equation for the data, and
• A prediction of the number of calories burned in an hour by a 140-pound person running at 9 miles per hour, with a comparison of your predicted value with the actual value of 953.

Speed (mph)	Calories
5	508
6	636
7	731
8	858

Short answer

• The given data can be used to write a linear equation that approximate the number of calories burned per hour.
• The scatter plot is shown below:
• 
  
• The model predicts that 140-pound person running at 9 miles per hour will burn 975 calories.
• The actual value is 953. The predicted value differs from the actual value by 2% only.

Step-by-step solution

Step-1 – Concept of scatter plot.

A scatter plot is a kind of plot where we use Cartesian coordinates to display values for typically two variables for a set of data.

Step-2 – Scatter plot.

Consider speed as x coordinate and calories as y coordinates.

The required plot is shown below:

Step-3 – Make the equation.

The given data can be used to write a linear equation that approximate the number of calories burned per hour.

The point slope form is $y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

Substitute $\left(x_1{y}_1\right)=(5,508) and \left(x_2{y}_2\right)= (8,858)$ into the above formula.

$\begin{array}{l}y-508=\frac{858-508}{8-5}(x-5)\\ y-508=116.67(x-5)\\ y-508=116.67x-583.35\\ y=116.67x-75.35\end{array}$

Step-4 – Make the prediction.

We need to determine the calories burned in an hour by a 140-pound person running at 9 miles per hours.

Put 9 for x into $y=116.67x-75.35$

$\begin{array}{l}y=116.67\left(9\right)-75.35\\ y=1050.03-75.35\\ y\approx 975\end{array}$

The model predicts that 140-pound person running at 9 miles per hour will burn 975 calories.

The actual value is 953. The predicted value differs from the actual value by 2% only.