Question

find an equation for the line below.

Explanation:

Step1: Identify two points

Let the two points on the line be $(-4,2)$ 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: $m=\frac{4 - 2}{2-(-4)}=\frac{2}{6}=\frac{1}{3}$.

Step3: Use the point - slope form

The point - slope form is $y - y_1=m(x - x_1)$. Using the point $(2,4)$ and $m = \frac{1}{3}$, we have $y - 4=\frac{1}{3}(x - 2)$.

Step4: Convert to slope - intercept form

Expand and simplify:
\[

$$\begin{align*} y-4&=\frac{1}{3}x-\frac{2}{3}\\ y&=\frac{1}{3}x-\frac{2}{3}+ 4\\ y&=\frac{1}{3}x+\frac{-2 + 12}{3}\\ y&=\frac{1}{3}x+\frac{10}{3} \end{align*}$$

\]

Answer:

$y=\frac{1}{3}x+\frac{10}{3}$