Question

https://www.ixl.com/math/level-j/write-a-linear-equation-from-a-graph
write your answer using integers, proper fractions, and improper fractions in simplest form.

Explanation:

Step1: Identify two points on the line

From the graph, we can see that the line passes through the points \((0, -5)\) (the y - intercept) and \((8, -6)\).

Step2: Calculate the slope \(m\)

The formula for the slope \(m\) between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
Let \((x_1,y_1)=(0, - 5)\) and \((x_2,y_2)=(8, - 6)\).
Then \(m=\frac{-6-(-5)}{8 - 0}=\frac{-6 + 5}{8}=\frac{-1}{8}\).

Step3: Write the equation in slope - intercept form

The slope - intercept form of a linear equation is \(y=mx + b\), where \(m\) is the slope and \(b\) is the y - intercept.
We know that \(m =-\frac{1}{8}\) and \(b=-5\) (since the line crosses the y - axis at \((0,-5)\)).
So the equation of the line is \(y=-\frac{1}{8}x-5\).

Answer:

\(y =-\frac{1}{8}x - 5\)