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)=-(1)/(2)x+6`

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=(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=(0-6)/(12-0)=-(1)/(2)`

Therefore, the function represented by the given graph is:

`f(x)=-(1)/(2)x+6`