Question

Given the function f(x) = 2x − 5 and g(x), which function has a greater slope?

x g(x)
2 0
4 5
6 10

1. f(x) has a greater slope.
2. g(x) has a greater slope.
3. The slopes of f(x) and g(x) are the same.
4. The slope of g(x) is undefined.

Answer 1

It’s 2 sorry if I’m wrong

Answer 2

Answer: The correct option is

(B) g(x) has a greater slope.

Step-by-step explanation: We are given the following two functions :

`f(x)=2x-5~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)`

and

x 2 4 6

g(x) 0 5 10

Comparing equation (i) of f(x) with the slope-intercept form y = mx+c, we get

`\textup{slope, m}=2.`

Now, we know that if a linear function contains two points (a, b) and (c, d), then its slope is given by

`m=(d-b)/(c-a).`

Since (2, 0) and (4, 5) are two points on g(x), so its slope will be

`m=(5-0)/(4-2)=(5)/(2)=2.5.`

Therefore, slope of f(x) = 2 and slope of g(x) = 2.5.

Thus, slope of g(x) is greater.

Option (B) is CORRECT.