Question

Which function is represented by the graph?

(A) f(x)=2x+6

(B) f(x)=−2x+6

(C) f(x)=−12x+6

(D) f(x)=12x+6

Answer 1

Answer:   $f(x)=-\frac{1}{2}x+6$

Step-by-step explanation:

The equation of the line in Slope-Intercept form is:

$y=mx+b$

Where "m" is the slope and "b" is hte y-intercept.

In this case, you can identify in the graph that the y-intercept is:

$y=6$

 By definition, the slope can be calculated with this formula:

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

Then, in order to find the slope, you can pick the points (0,6) and (12,0) and say that:

$y_2=0\\y_1=6\\\\x_2=12\\x_1=0$

So, substituting these values into the formula, you get:

$m=\frac{0-6}{12-0}=-\frac{1}{2}$

Therefore, the function represented by the given graph is:

$f(x)=-\frac{1}{2}x+6$