Question

Jamila has a weather station in her backyard. She uses a rain gauge to track the total rainfall during two storms.

Answer the questions to compare the storms.

Part A
Jamila graphs the function describing Monday's rainfall. Is the graph linear or nonlinear? How do you know?

Part B
What is the real-world meaning of the slope of the graph?

Part C
Next, Jamila graphs the function describing Thursday's rainfall. Is this graph linear or nonlinear? How do you know?

Part D
What does the y-intercept of the graph of Monday's storm mean? Does the y-intercept of the graph of Thursday's storm have the same meaning?
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Answer 1

Part A: Monday's rainfall is linear, increasing at a steady rate.

Part B: Slope shows how fast precipitation is increasing.

Part C: Thursday's rainfall is nonlinear, not changing at a constant rate.

Part D: Y-intercept shows initial precipitation for both storms.

Part A:

Explanation: The graph shows a straight line, which means that the precipitation increases at a steady rate over time. This is a characteristic of a linear function.

The graph of Monday's rainfall is linear.

Part B:

The slope of the graph represents the rate of change of the precipitation over time. In this case, the slope is positive, which means that the precipitation is increasing as time goes on. The steeper the slope, the faster the precipitation is increasing.

Part C:

The graph shows a curve, which means that the precipitation is not changing at a constant rate over time. This is a characteristic of a nonlinear function.

The graph of Thursday's rainfall is nonlinear.

Part D:

The y-intercept of the graph of Monday's storm represents the amount of precipitation that has already fallen when Jamila starts tracking the storm. The y-intercept of the graph of Thursday's storm has the same meaning.