Question

find an equation for the line below.

Explanation:

Step1: Identify two points on the line

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

Step2: Calculate the slope (\(m\))

The formula for slope is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
Substituting the points \((x_1,y_1)=(-2, -3)\) and \((x_2,y_2)=(6, -1)\):
\(m=\frac{-1 - (-3)}{6 - (-2)}=\frac{-1 + 3}{6 + 2}=\frac{2}{8}=\frac{1}{4}\)

Step3: Use point - slope form to find the equation

The point - slope form is \(y - y_1=m(x - x_1)\). Let's use the point \((6, -1)\) and \(m = \frac{1}{4}\).
\(y-(-1)=\frac{1}{4}(x - 6)\)
\(y + 1=\frac{1}{4}x-\frac{6}{4}\)
\(y=\frac{1}{4}x-\frac{3}{2}-1\)
\(y=\frac{1}{4}x-\frac{3 + 2}{2}\)
\(y=\frac{1}{4}x-\frac{5}{2}\) (We can also verify with the other point. Let's check for \(x=-2\): \(y=\frac{1}{4}(-2)-\frac{5}{2}=-\frac{1}{2}-\frac{5}{2}=-3\), which matches the point \((-2,-3)\))

Answer:

\(y=\frac{1}{4}x-\frac{5}{2}\)