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Tom is comparing the slopes of the following two functions. Function 2 Function 1 A linear function with a rate of change of negative 3 and crosses the y-axis at 1. y = -x + 5 Tom finds the slope of Function 1 to be -3 and the slope of Function 2 to be -1. Tom concludes that since -3 < -1, Function 2 has a steeper slope. Explain why Tom's conclusion is incorrect and show how to find which function has a steeper slope.

Tom is comparing the slopes of the following two functions. Function 2 Function 1 A linear function with a rate of change of negative 3 and crosses the y-axis at 1. y = -x + 5 Tom finds the slope of Function 1 to be -3 and the slope of Function 2 to be -1. Tom concludes that since -3 < -1, Function 2 has a steeper slope. Explain why Tom's conclusion is incorrect and show how to find which function has a steeper slope.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Tom is comparing the slopes of the following two functions. **Function 1** A linear function with a rate of change of negative 3 and crosses the y-axis at 1. **Function 2** \( y = -x + 5 \) Tom finds the slope of Function 1 to be -3 and the slope of Function 2 to be -1. Tom concludes that since -3 < -1, Function 2 has a steeper slope. Explain why Tom’s conclusion is incorrect and show how to find which function has a steeper slope.
Transcribed Image Text:Tom is comparing the slopes of the following two functions. **Function 1** A linear function with a rate of change of negative 3 and crosses the y-axis at 1. **Function 2** \( y = -x + 5 \) Tom finds the slope of Function 1 to be -3 and the slope of Function 2 to be -1. Tom concludes that since -3 < -1, Function 2 has a steeper slope. Explain why Tom’s conclusion is incorrect and show how to find which function has a steeper slope.
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