To analyze Rita's study time in relation to the calories burned, we can derive the answers based on the properties of a linear graph.
(a) To find out how many minutes Rita studies per calorie burned, we need to determine the ratio of minutes to calories burned. From the graph, we can identify two points that represent the relationship between the number of minutes (x-axis) and calories burned (y-axis).
Let's assume the two points on the graph are:
- Point A: (x1, y1) = (0, 0) (where she started)
- Point B: (x2, y2) = (200, 80) (an arbitrary point on the graph)
The change in y over the change in x gives us:
- Δy (Calories burned) = 80 - 0 = 80
- Δx (Minutes studied) = 200 - 0 = 200
Now, minutes per calorie burned can be calculated as: \[ \text{Minutes per calorie} = \frac{\text{Δx}}{\text{Δy}} = \frac{200 \text{ minutes}}{80 \text{ calories}} = \frac{200}{80} = 2.5 \text{ minutes per calorie} \]
So, the answer to part (a) is: 2.5 minutes per calorie burned.
(b) The slope of the graph represents the ratio of the change in the y-values (calories burned) to the change in the x-values (minutes studied). This can be calculated similarly from the two points we used:
The slope \( m \) can be calculated as: \[ m = \frac{\Delta y}{\Delta x} = \frac{80}{200} = 0.4 \]
Thus, the slope of the graph is: 0.4 (which means for every 1 minute studied, Rita burns 0.4 calories).
In summary: (a) 2.5 minutes per calorie burned. (b) The slope of the graph is 0.4.