Answer:
[tex]\sf y =\dfrac{-11}{8}x +\dfrac{13}{8}[/tex]
Step-by-step explanation:
Here, m is the slope and b is the y-intercept.
( -1, 3) ; x₁ = -1 & y₁ = 3
(7, -8) ; x₂ = 7 & y₂ = -8
Slope can be obtained by the formula:
[tex]\sf \boxed{\bf Slope = \dfrac{y_2-y_1}{x_2-x_1}}[/tex]
[tex]\sf =\dfrac{-8-3}{7-[-1]}\\\\\\=\dfrac{-8-3}{7+1}\\\\\\=\dfrac{-11}{8}[/tex]
Now, we can find the y-intercept,
[tex]\sf y = \dfrac{-11}{8}x + b\\\\Substitute \ any \ one \ of \ the \ point \ in \ the \ above \ equation.\\\\\text{Here, we are substituting (-1 ,3)}\\\\3 = \dfrac{-11}{8}*(-1) + b\\\\3 = \dfrac{11}{8}+b\\\\b = 3 - \dfrac{11}{8}\\\\b = \dfrac{3*8}{1*8}-\dfrac{11}{8}\\\\b= \dfrac{24-11}{8}\\\\b= \dfrac{13}{8}[/tex]
Slope-intercept form:
[tex]\sf y =\dfrac{-11}{8}x +\dfrac{13}{8}[/tex]