Question

find an equation for the line below.

Explanation:

Step1: Identify two points

Let's take two points on the line, say $(- 6,2)$ and $(2,4)$.

Step2: Calculate the slope $m$

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

Step3: Use the point - slope form

The point - slope form is $y - y_1=m(x - x_1)$. Using the point $(2,4)$ and $m = \frac{1}{4}$, we have $y - 4=\frac{1}{4}(x - 2)$.

Step4: Convert to slope - intercept form

Expand the right - hand side: $y-4=\frac{1}{4}x-\frac{1}{2}$. Then add 4 to both sides: $y=\frac{1}{4}x-\frac{1}{2}+4=\frac{1}{4}x+\frac{-1 + 8}{2}=\frac{1}{4}x+\frac{7}{2}$.

Answer:

$y=\frac{1}{4}x+\frac{7}{2}$