Question

1. apply math models the graph shows the number of calories natalia burned while running.

a. what is the slope of the line?
b. what does the slope tell you?
(graph: x-axis labeled time (minutes) from 0 to 10, y-axis labeled calories from 0 to 70, line passing through (0,0) and other points)

Explanation:

Part a:

Step1: Recall slope formula

The slope \( m \) of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \).

Step2: Identify two points on the line

From the graph, we can see that the line passes through \((0, 0)\) and \((1, 10)\) (or other points like \((2, 20)\), etc.). Let's use \((0, 0)\) as \((x_1, y_1)\) and \((1, 10)\) as \((x_2, y_2)\).

Step3: Calculate the slope

Substitute into the slope formula: \( m=\frac{10 - 0}{1 - 0}=\frac{10}{1} = 10 \).

The slope represents the rate of change of calories burned with respect to time. A slope of 10 means that Natalia burns 10 calories per minute while running.

Answer:

The slope of the line is \( 10 \).

Part b: