Question

write your answer using integers, proper fractions, and improper fractions in simple form.

Explanation:

Assuming the problem is to find the equation of the line (since it's a graph of a line), let's proceed:

Step1: Identify two points

From the graph, the line passes through \((0, 4)\) (y-intercept) and let's take another point, say \((8, 2)\).

Step2: Calculate the slope \(m\)

The slope formula is \(m = \frac{y_2 - y_1}{x_2 - x_1}\). Using \((0, 4)\) as \((x_1, y_1)\) and \((8, 2)\) as \((x_2, y_2)\):
\(m = \frac{2 - 4}{8 - 0} = \frac{-2}{8} = -\frac{1}{4}\)

Step3: Use slope-intercept form \(y = mx + b\)

We know \(m = -\frac{1}{4}\) and \(b = 4\) (from the y-intercept \((0, 4)\)):
\(y = -\frac{1}{4}x + 4\)

Answer:

The equation of the line is \(y = -\frac{1}{4}x + 4\)