Answer:
[tex]2x-3y=19[/tex]
Step-by-step explanation:
we have the ordered pairs
(8, –1) and (2, –5)
Find the slope
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
substitute the values in the formula
[tex]m=\frac{-5+1}{2-8}[/tex]
[tex]m=\frac{-4}{-6}[/tex]
simplify
[tex]m=\frac{2}{3}[/tex]
The equation of the line in point slope form is
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=\frac{2}{3}[/tex]
[tex]point\ (8,-1)[/tex]
substitute
[tex]y+1=\frac{2}{3}(x-8)[/tex]
Convert to standard form
The equation of the line in standard form is equal
[tex]Ax+By=C[/tex]
where
A is a positive integer
B and C are integers
we have
[tex]y+1=\frac{2}{3}(x-8)[/tex]
Multiply by 3 both sides to remove the fraction
[tex]3y+3=2(x-8)[/tex]
apply distributive property right side
[tex]3y+3=2x-16[/tex]
Group the variables in one side and the constants in the other side
[tex]2x-3y=3+16[/tex]
[tex]2x-3y=19[/tex] ---> equation in standard form
