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

Answer 1

Slope of both the functions is the same.

Explanation:

We are given two functions so we will find the slope for each of them to compare with each other.

We know that Xavier runs the 400m race in 50 seconds,

so, slope of f(x):
`(400)/(50) =8`

For finding the slope of g(x), we will take any two consecutive points and find their slope.

(5, 12) and (7, 28)

Slope of g(x) =
`(28-12)/(7-5) =(16)/(2) =8`

Therefore, we can conclude that slope of both of the functions, f(x) and g(x), is the same.

Answer 2

They both have the same slope.

Step by step explanation

Let's find the slope of f(x).

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

Slope of f(x) = 400/50 = 8

Now let's find the slope of g(x)

Let's take two points from the table and find the slope of g(x)

Let's take (3, -4) and (5, 12)

Slope of g(x) = (y2 - y1)/(x2 - x1)

Here x1 = 3, y1 = -4, x2 = 5 and y2 = 12

g(x) = (12 - (-4)) / (5 - 3)

g(x) = (12 +4) / (2)

g(x) = 16/2

g(x) = 8

The slope of g(x) = 8 and also f(x) = 8.

Therefore, the slope of both functions (f(x) and g(x)) are the same.

Answer: They both have the same slope.

Thank you. :)