Question

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Answer 1

Answer: Choice D) Slopes are the same

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Explanation:

The graph of f(x) is a straight line through the two points (0,3) and (1,1). Those points are the left and right points respectively.

Start at (0,3). To get to (0,1), we move 2 units down and 1 unit to the right. Think of the "2 units down" as a "rise of -2". Negative rise means you're really falling.

So the slope of f(x) is
slope = rise/run = -2/1 = -2
slope = -2

The slope of g(x) is also -2

Note how y = -2x-5 is in y = mx+b form
we see that m = -2 is the slope
b = -5 is the y intercept

So that shows why the two functions have the same slope.