To analyze the relationship between the number of minutes Amanda has run (x) and the calories burned (y), we can look at the given data points from the graph. Since the relationship varies directly, we can express it as:
\[ y = kx \]
where \( k \) is the constant of proportionality (i.e., calories burned per minute).
(a) How many calories is Amanda burning per minute?
From the graph, we can select two data points to find the rate of calories burned per minute. Let's use the points (25 minutes, 100 calories) and (50 minutes, 200 calories).
Using the formula for the slope \( k \):
\[ k = \frac{y_2 - y_1}{x_2 - x_1} \]
Using (x₁, y₁) = (25, 100) and (x₂, y₂) = (50, 200):
\[ k = \frac{200 - 100}{50 - 25} = \frac{100}{25} = 4 \]
So, Amanda is burning 4 calories per minute.
(b) What is the slope of the graph?
The slope of the graph also represents the calories burned per minute, which we've already calculated using the same rate \( k \):
The slope is 4.
Thus, the answers are: (a) 4 calories (b) 4