Answer:
[tex]y=-2x+2a+b[/tex]
Step-by-step explanation:
step 1
Find the slope
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
we have the ordered pairs
(a, b), (a + 2, b - 4)
substitute the values in the formula
[tex]m=\frac{b-4-b}{a+2-a}[/tex]
[tex]m=\frac{-4}{2}[/tex]
[tex]m=-2[/tex]
step 2
Find the equation of the line in point slope form
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=-2[/tex]
[tex]point\ (a,b)[/tex]
substitute
[tex]y-b=-2(x-a)[/tex]
step 3
Convert to slope-intercept form
[tex]y=mx+b[/tex]
isolate the variable y
[tex]y-b=-2x+2a[/tex]
[tex]y=-2x+2a+b[/tex]
