Question

Jina is running. The number of minutes she has run varies directly with the number of calories she has burned. See the graph below.

How many calories is Jina burning per minute ?

What is the slope of the graph ?

Answer 1

1. Difference in y-values (calories burned):
`\( 15 - 5 = 10 \)`

2. Difference in x-values (minutes):
`\( 150 - 50 = 100 \)`

3. Slope (calories burned per minute):
`\( (10)/(100) = 0.1 \)`

To find out how many calories Jina is burning per minute and the slope of the graph given the points (150, 15) and (50, 5), we'll do the following calculations:

1. Calculate the slope of the line, which also represents the calories burned per minute. This is done using the formula for the slope (m) between two points on a line:

`\[ m = (y_2 - y_1)/(x_2 - x_1) \]`

2. Substitute the given points (150, 15) and (50, 5) into the slope formula:

`\[ m = (15 - 5)/(150 - 50) \]`

3. Simplify the difference in the y-values (calories burned) and the x-values (minutes):

`\[ m = (10)/(100) \]`

4. Calculate the slope, which gives the rate at which calories are burned per minute:

`\[ m = (1)/(10) \]`

5. Convert the slope to a decimal to find out the exact number of calories burned per minute.

Let's perform the calculations.

The slope of the graph is 0.1, which represents the rate at which calories are burned per minute. This means that Jina is burning 0.1 calories per minute. Here are the step-by-step calculations:

1. Difference in y-values (calories burned):
`\( 15 - 5 = 10 \)`

2. Difference in x-values (minutes):
`\( 150 - 50 = 100 \)`

3. Slope (calories burned per minute):
`\( (10)/(100) = 0.1 \)`

Answer 2

She burns 5 calories per minute and the slope is 1/2