Question

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

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)