Question

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?

Answer 1

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**.