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
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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

Answer:

b. both functions have a negative slope

Step-by-step 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,

$m=\frac{y_2-y_1}{x_2-x_1}$.

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

$m=\frac{6-7}{2-0}$

$m=-\frac{1}{2}$.

We can see that both functions have a negative slope.

The correct answer is B.