Question

The function f(x) is shown in this graph.

The function g(x) = –6x – 5. Compare the slopes.

A. The slope of f(x) is undefined and the slope of g(x) is negative.
B. The slope of f(x) is less than the slope of g(x).
C. The slope of f(x) is greater than the slope of g(x).
D. The slope of f(x) is the same as the slope of g(x).

Answer 1

The function f(x) goes down by two and over by one:
slope = rise/run = -2/1 = -2.

The slope of f(x) is -2, while the slope of g(x) is -6.

Since -2 is a greater number than -6, the answer is:
C) The slope of f(x) is greater than the slope of g(x).

Answer 2

You can calculate the slope of the function f(x) shwon in the graph with the formula:

rise
slope = -------
run

rise = change in y-direction = Δy

run = change in x - direction = Δx

Δy y2 - y1 [1 - 3] - 2
slope = ------ = --------- = -------- = ----- - 2
Δx x2 - x1 [1 - 0] 1

2) The slope of the funtion g(x) defined as - 6x - 5 is the coefficient of x, which is - 6.

So, compare: - 2 > - 6, i.e. the slope of f(x) is greater than the slope of g(x).

Anxwer: the slope of f(x) is greater than the slope of g(x)