Question

uation for the line below.

Explanation:

Step1: Identify two points on the line

Let the two points be $(-2,1)$ and $(4,5)$.

Step2: Calculate the slope $m$

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Substituting the points $(-2,1)$ and $(4,5)$ gives $m=\frac{5 - 1}{4-(-2)}=\frac{4}{6}=\frac{2}{3}$.

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

Using the point $(-2,1)$ and $m = \frac{2}{3}$, we have $y - 1=\frac{2}{3}(x+2)$.

Step4: Convert to slope - intercept form $y=mx + b$

Expand the point - slope form: $y-1=\frac{2}{3}x+\frac{4}{3}$. Then $y=\frac{2}{3}x+\frac{4}{3}+1=\frac{2}{3}x+\frac{4 + 3}{3}=\frac{2}{3}x+\frac{7}{3}$.

Answer:

$y=\frac{2}{3}x+\frac{7}{3}$