use this graph of g to find g(6).

Explanation:

Step1: Locate x - value on graph

Locate x = 6 on the x - axis.

Step2: Find corresponding y - value

Move vertically from x = 6 until you hit the graph of the function g. Then move horizontally to find the y - value. Since the graph of the function g is a line segment starting at (4,0) and going to (8,10), we first find the equation of the line. The slope $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{10 - 0}{8 - 4}=\frac{10}{4}=\frac{5}{2}$. Using the point - slope form $y - y_1=m(x - x_1)$ with the point $(4,0)$, we have $y-0=\frac{5}{2}(x - 4)$. When $x = 6$, $y=\frac{5}{2}(6 - 4)=\frac{5}{2}\times2 = 5$.

Answer:

5