Question

write the equation of this line in slope-intercept form.
write your answer using integers, proper fractions, and improper fractions in simplest form

Explanation:

Step1: Recall slope - intercept form

The slope - intercept form of a line is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept.

Step2: Find the y - intercept (\(b\))

The line crosses the y - axis at \((0,5)\), so \(b = 5\).

Step3: Calculate the slope (\(m\))

We can use two points on the line. We know \((0,5)\) is on the line, and let's find another point. When \(x = 8\), \(y = 1\) (from the graph). The formula for slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(0,5)\) and \((x_2,y_2)=(8,1)\). Then \(m=\frac{1 - 5}{8 - 0}=\frac{- 4}{8}=-\frac{1}{2}\).

Step4: Write the equation

Substitute \(m =-\frac{1}{2}\) and \(b = 5\) into the slope - intercept form \(y=mx + b\). We get \(y=-\frac{1}{2}x + 5\).

Answer:

\(y =-\frac{1}{2}x + 5\)