Question

Which of the following functions has a steeper slope?

Function A: y = -3x + 6
Function B: y = 2x - 5
A) Function A
B) Function B
C) Both functions have the same slope
D) None of the above

Answer 1

Function A has a steeper slope than Function B because the absolute value of its slope (-3) is greater than that of Function B (2), showing that Function A will have the steeper line on a graph.

Step-by-step explanation:

To determine which function has the steeper slope, we compare the coefficients of x in the equations of Function A: y = -3x + 6 and Function B: y = 2x - 5. The slope of a line in the slope-intercept form, y = mx + b, is represented by the coefficient m.

For Function A, the slope is -3. For Function B, the slope is 2. In terms of absolute value, a slope of -3 is steeper than a slope of 2 because |-3| > |2|. Therefore, Function A has a steeper slope than Function B.

Additionally, it's important to note that Function A is a decreasing line due to its negative slope, while Function B is an increasing line due to its positive slope. However, the question specifically asks about the steepness of the slope, which is based on the magnitude of the slope's coefficient regardless of its sign.

The correct answer to the question is A) Function A, as it has a steeper slope than Function B.