Question

find an equation for the line below.

Explanation:

Step1: Identify two points

From the graph, we can see two points: \((-2, -1)\) and \((6, -3)\).

Step2: Calculate the slope

The slope \(m\) is given by \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Substituting the points \((x_1,y_1)=(-2,-1)\) and \((x_2,y_2)=(6,-3)\), we get \(m=\frac{-3 - (-1)}{6 - (-2)}=\frac{-2}{8}=-\frac{1}{4}\).

Step3: Use point - slope form

Using the point - slope form \(y - y_1=m(x - x_1)\) with the point \((-2,-1)\) and \(m =-\frac{1}{4}\).
\(y-(-1)=-\frac{1}{4}(x - (-2))\)
\(y + 1=-\frac{1}{4}(x + 2)\)
\(y=-\frac{1}{4}x-\frac{1}{2}-1\)
\(y=-\frac{1}{4}x-\frac{3}{2}\)

Answer:

\(y =-\frac{1}{4}x-\frac{3}{2}\)