Question

Below are two different functions, f(x) and g(x). What can be determined about their slopes?
f(x)= 4x + 2
A) function f(x) has a larger slope
B) the function g(x) has a larger slope
C) they both have the same slope
D) the relationship between slopes cannot be determined

Answer 1

Answer: B) the function g(x) has a larger slope

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Explanation:

The slope of f(x) is 4, since the equation y = 4x+2 has slope m = 4. Compare this to y = mx+b.

The slope of g(x) is 5. Note how if we started at (0,-2) on the red line and moved up 5 and to the right 1, we arrive at (1,3) which is another point on the red line. You could use the slope formula

m = (y2-y1)/(x2-x1)

to get the same result.

Since the slope of f(x) is 4 and the slope of g(x) is 5, we see that g(x) has a larger slope. The g(x) line is steeper compared to f(x).