Question

martina is running. the number of minutes she has run varies directly with the number of calories she has burned. use the graph below.

(a) how many calories is martina burning per minute?
______ calorie(s)

(b) what is the slope of the graph?
______

Explanation:

Step1: Analyze Direct Variation

Since minutes and calories are directly proportional, the graph is a straight line through the origin. The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$. Let's pick two points, say (0, 0) and (200, 50) (assuming from the graph, as it's a direct variation).

Step2: Calculate Calories per Minute (a)

Calories per minute is the rate, which is the slope. Using points (0,0) and (200,50):
$\frac{50 - 0}{200 - 0} = \frac{50}{200} = 0.25$ calories per minute.

Step3: Determine Slope (b)

The slope of a direct variation graph (through origin) is the same as the rate. So slope $= 0.25$ (or $\frac{1}{4}$).

Answer:

(a) 0.25
(b) 0.25