Answer:
2x - 3y = 19
Step-by-step explanation:
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points (8, -1) and (2, -5). Substitute:
[tex]m=\dfrac{-5-(-1)}{2-8}=\dfrac{-4}{-6}=\dfrac{2}{3}[/tex]
The point-slope form of an equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
Substitute:
[tex]y-(-1)=\dfrac{2}{3}(x-8)[/tex]
[tex]y+1=\dfrac{2}{3}(x-8)[/tex] → the point-slope form
Convert to the standard form: [tex]Ax+By=C[/tex]
[tex]y+1=\dfrac{2}{3}(x-8)[/tex] multiply both sides by 3
[tex]3y+3=2(x-8)[/tex] use the distributive property a(b+c) = ab+ ac
[tex]3y+3=2x-16[/tex] subtract 3 from both sides
[tex]3y=2x-19[/tex] subreact 2x from both sides
[tex]-2x+3y=-19[/tex] change the signs
[tex]2x-3y=19[/tex] → the standard form
