Question

Below are two different functions f(x) and g(x). What can be determined about their slopes

f(x) Xavier runs the 400m race in 50 seconds.

X | g(x)
3 | -4
5 | 12
7 | 28

A. The 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

C. They both have the same slope.

To determine the slope of f(x), we divide 400 by 50 to determine how fast Xavier runs per second, which is the rate of change

So slope of f(x) = 400/50 = 8

For g(x), the slope can be determined by using two given points from the table and plugging them into the formula (y2-y1)/(x2-x1)

So if we plug in the first two points, we get

(12+4)/(5-3) = 16/2 = 8


Slope of f(x) = 8
Slope of g(x) = 8