Question

Diane is walking. The number of minutes she has walked varies directly with the number of calories she has burned. See the graph below.(a) how many minutes does Diane walk per calorie burned(b) what is the slope of the graph

Answer 1

Given: The graph showing the number of minutes Diane walked against the number of calories burned

To Determine: (a)how many minutes does Diane walk per calorie burned (b) the slope of the graph

Solution:

Step 1: Locate at least two points fom the graph

The points located is as shown below

So, at 10 minutes, 100 calories was burned. Also, at 20 minutes, 200 calories was burned

Therefore, the number of minutes Diane walk per calorie would be

`(10)/(100)=(1)/(10)=0.1minutes`
`(20)/(200)=0.1minutes`

Hence, the number of minutes Diane walk per calorie burned is 0.1 minutes

(b) To Determine: The slope of the graph

The slope of a straight line graph given two points can be calculated by the formula

`\begin{gathered} A(x_1,y_1);B(x_2,y_2) \\ slope(s)=(y_2-y_1)/(x_2-x_1) \end{gathered}`

Apply the formula to find the slope of the graph from the two points selected earlier

`\begin{gathered} PointA:(100,10) \\ PointB:(200,20) \end{gathered}`
`s=((20-10)minutes)/((200-100)calories)=(10minutes)/(100calories)=0.1minutes\text{ per calorie}`

Hence

(a) The number of minutes Diane walk per calorie burned is 0.1 minutes

(b) The slope of the graph is 0.1 minutes per calorie