Question

use the graph of g to find g(5).
g(5) = \square

Explanation:

Step1: Identify the line for x=5

First, locate the segment of the graph that includes \(x=5\). This is the line passing through \((0,0)\) and \((8,5)\).

Step2: Find the slope of the line

Calculate the slope \(m\) using the two points:
\(m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{5 - 0}{8 - 0} = \frac{5}{8}\)

Step3: Write the line's equation

Using the y-intercept \(b=0\), the equation is \(y = \frac{5}{8}x\).

Step4: Substitute x=5 into the equation

Compute \(g(5)\):
\(g(5) = \frac{5}{8} \times 5 = \frac{25}{8} = 3.125\)

Answer:

\(3.125\) or \(\frac{25}{8}\)