Question

find an equation for the line below.

Explanation:

Step1: Find two points on the line

From the graph, two points are \((-1,2)\) and \((3,4)\).

Step2: Calculate the slope \(m\)

Use the slope formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
Substitute \(x_1=-1,y_1 = 2,x_2=3,y_2 = 4\) into the formula:
\(m=\frac{4 - 2}{3-(-1)}=\frac{2}{4}=\frac{1}{2}\)

Step3: Use the point - slope form \(y - y_1=m(x - x_1)\)

Take the point \((-1,2)\) and \(m = \frac{1}{2}\).
\(y - 2=\frac{1}{2}(x+1)\)

Step4: Simplify to slope - intercept form \(y=mx + b\)

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

Answer:

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