Question

Maria compared the slope of the function f(x)=(-6x-21) to the slope of the linear function that fits the values in the table below.

x -4 -2 0 2 4
----------------------------------------------------
g(x) 9 8 7 6 5


A. both functions have a positive slope.

b. both functions have a negative slope

c. function f(x) has a positive slope, while function g(x) has a negative slope.

Answer 1

b. both functions have a negative slope

Explanation:

The given function is

`f(x)=-6x-21`

This function is of the form
`y=mx+b`, where
`m=-6` is the slope and
`b=-21` is the y-intercept.

We can also determine the slope of the function in the table using any two points, say
`(0,7)\:and\:(2,6)`.

The slope formula is given by,

`m=(y_2-y_1)/(x_2-x_1)`.

If
`(x_1,y_1)=(0,7)\:and\:(x_2,y_2)=(2,6)`, then,

`m=(6-7)/(2-0)`

`m=-(1)/(2)`.

We can see that both functions have a negative slope.

The correct answer is B.