[tex]m = \frac{8 - 2}{6 - ( - 3)} \\ m = \frac{6}{6 + 3} \\ m = \frac{6}{9} \\ m = \frac{2}{3} [/tex]
The slope is 2/3.
[tex]y = mx + b[/tex]
where m = slope and b = y-intercept. Substitute the value of m in slope-intercept form.
[tex]y = \frac{2}{3} x + b[/tex]
I will use (-3,2) instead.
[tex]2 = \frac{2}{3} ( - 3) + b \\ 2 = - 2 + b \\ 2 + 2 = b \\ 4 = b[/tex]
The y-intercept is (0,4). Then rewrite the equation by substituting the b-value and slope in slope-intercept form.
[tex]y = \frac{2}{3} x + 4[/tex]
[tex] \large \boxed{y = \frac{2}{3} x + 4}[/tex]
