Answer:
[tex]\huge\boxed{y=-6x+28}[/tex]
Step-by-step explanation:
The point-slope form of an equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
[tex]m[/tex] - slope
[tex](x_1;\ y_1)[/tex] - point on a line
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex](x_1;\ y_1);\ (x_2;\ y_2)[/tex] - points on a line
We have two points:
[tex](8;\ -20);\ (5;\ -2)[/tex]
Calculate the slope:
[tex]m=\dfrac{-2-(-20)}{5-8}=\dfrac{-2+20}{-3}=\dfrac{18}{-3}=-6[/tex]
Substitute to the equation of a line:
[tex]y-(-20)=-6(x-8)[/tex]
[tex]y+20=-6x+48[/tex] subtract 20 from both sides
[tex]y=-6x+28[/tex]
