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Answer:
C. the slope of f(x) is less ...
Step-by-step explanation:
"Slope" is a signed number, so comparison using words like "less than" or "greater than" are expected to be used as they are in the context of signed numbers.
The slope of f(x) is the "rise" divided by the "run" of the graph. From left to right, the two points on the graph of f(x) have a "rise" of -2 for a "run" of +1. The slope of f(x) is ...
m = rise/run = -2/1 = -2
The slope of g(x) is the coefficient of the x-term, -7.
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In the context of signed numbers, the slope of f(x) is -2 and the slope of g(x) is -7. We know -2 is greater than -7, so the slope of f(x) is greater than the slope of g(x).
However ...
In the real world, the slope of a hill is measured in the same way: rise is divided by run. The slope of a hill is always a positive number, because we're not concerned about what compass direction we're going. We're only concerned with how high we need to raise our foot to take the next step up the hill. That is, we're concerned with the "steepness" of the slope, its magnitude.
In that sense, the function g(x) changes 7 units for a change in x of 1 unit, and the function f(x) changes 2 units for the same change in x. Considered in this way, the "steepness" of the g(x) line is greater than that of the f(x) line. We can say the slope of f(x) is less than the slope of g(x).
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If the question is asking about the algebraic relation of the slopes of the lines, then the answer is ...
A. The slope of f(x) is greater ... (-2 > -7)
If the question is asking about the steepness of the lines, as we expect is the case, then the answer is ...
C. The slope of f(x) is less ... (2 < 7)
