Raina is walking. The number of calories she has burned varies directly with the number of minutes she has walked. See the graph below.

y
4
8
12
16
20
24
28
32
36
x
2
4
6
8
10
12
14
16
18
0
Caloriesburned
Numberofminutes

(a) How many calories is Raina burning per minute?
calorie(s)
(b) What is the slope of the graph?

1 answer

To determine how many calories Raina is burning per minute and the slope of the graph, we can analyze the data based on the provided information.

(a) Calories Burned Per Minute

From the graph, we can observe specific data points. Let's assume that you have the points shown on the graph:

  • For 2 minutes, she burns 4 calories.
  • For 4 minutes, she burns 8 calories.
  • For 6 minutes, she burns 12 calories.

From these points, we can see that for each increase of 2 minutes, the calories burned increases by 4 calories.

To find calories burned per minute:

  • From the points: \( \frac{4 \text{ calories}}{2 \text{ minutes}} = 2 \text{ calories per minute} \)

Thus, Raina is burning 2 calories per minute.

(b) Slope of the Graph

The slope of a line on a graph is defined as the change in the y-coordinates divided by the change in the x-coordinates (rise over run). In this case:

  • Rise (change in calories burned): From 4 calories to 8 calories = \( 8 - 4 = 4 \)

  • Run (change in time in minutes): From 2 minutes to 4 minutes = \( 4 - 2 = 2 \)

Now, we calculate the slope: \[ \text{slope} = \frac{\text{rise}}{\text{run}} = \frac{4 \text{ calories}}{2 \text{ minutes}} = 2 \]

Thus, the slope of the graph is 2.

In conclusion:

  • (a) Raina is burning 2 calories per minute.
  • (b) The slope of the graph is 2.