Question

(0,2)-5The function g(x) = -3x - 6. Compare the slopes.A. The slope of f(x) is the same as the slope of g(x).B. The slope of f(x) is undefined, and the slope of g(x) is negative.Ο ΟC. The slope of f(x) is greater than the slope of g(x).D. The slope of f(x) is less than the slope of g(x).

Answer 1

To solve the exercise, first we are going to find the slope of the function f(x). Since we have a graph of the function, we can see two points through which the line passes:

`\begin{gathered} (x_1,y_1)=(0,2) \\ (x_2,y_2)=(1,-1) \end{gathered}`

Now we can use this formula to find the slope:

`\begin{gathered} m=(y_(2)-y_(1))/(x_(2)-x_(1)) \\ \text{ Where m is the slope and} \\ (x_1,y_1)\text{ and }(x_2,y_2)\text{ are two points through which the line passes} \end{gathered}`
`\begin{gathered} m_(f(x))=(-1-2)/(1-0) \\ m_(f(x))=(-3)/(1) \\ m_(f(x))=-3 \end{gathered}`

Then, the slope of the function f(x) is -3.

On the other hand, the function g(x) also describes a line and is written in slope-intercept form, that is:

`\begin{gathered} y=mx+b\Rightarrow\text{ slope-intercept form} \\ \text{ Where m is the slope and} \\ b\text{ is the y-intercept of the line} \end{gathered}`

Then, you can see that the slope of the function g(x) is -3, because

`\begin{gathered} g(x)=-3x-6 \\ m_(g(x))=-3 \\ \text{and} \\ b=-6 \end{gathered}`

Therefore, the slope of f(x) is the same as the slope of g(x) and the correct answer is option A.