Question 103·Hard·Algebra

After you have the slope, plug one labeled point into $y=mx+b$ to solve for $b$.

Use $y=2f(x)+x$. Subtract $x$ from both sides to get $2f(x)=y-x$, then divide by 2.

Enter the points from the graph: A=(-7,6) and B=(5,-4).

Compute the slope with m=(-4-6)/(5-(-7)), then graph the line using point-slope form: y=m(x-5)-4.

Since $y=2f(x)+x$, enter f(x)=(m(x-5)-4 - x)/2 and simplify the result to match an answer choice.

From the graph, the line passes through $A(-7,6)$ and $B(5,-4)$. The slope is

Use $B(5,-4)$ in $y=mx+b$:

So the graphed line is

Since the line is the graph of $y=2f(x)+x$, substitute $y=-\frac{5}{6}x+\frac{1}{6}$:

Subtract $x$ from both sides:

Divide by 2:

Therefore, $f(x) = -\tfrac{11}{12} x + \tfrac{1}{12}$.