Question

Question 6 Samantha purchases a package of sugar cookies. The nutrition label states that each serving size of 3 cookies contains 160 Calories. Samantha creates the graph to the right showing the number of cookies eaten and the number of Calories consumed.

Answer 1

Each serving size of 3 cookies contains 160 calories.

Samantha creates the graph to the right showing the number of cookies eaten and the number of Calories consumed

As you can see from the graph, these data points can be connected by a straight line.

A straight line means that it must be a linear function.

In a linear function, the rate of change of output (y) with respect to input (x) remains constant.

The number of calories (y) depends upon the number of cookies (x) and the rate at which y changes with respect to x is called slope and is given by

`\text{slope}=(y_2-y_1)/(x_2-x_1)`

You can choose any two points from the graph and find the slope of the graph.

The slope remains constant no matter which two points you select.

Therefore, the conclusion is

It is appropriate for Samantha to draw a line through the points on the graph since a straight line means that it is a linear function so the rate of change of output (y) with respect to input (x) remains constant.