Answer:
[tex]y=-x+1[/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
(2,-1) and (-4,5)
substitute the values
[tex]m=\frac{5+1}{-4-2}[/tex]
[tex]m=\frac{6}{-6}[/tex]
[tex]m=-1[/tex]
step 2
Find the equation of the line in point slope form
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=-1[/tex]
[tex]point\ (2,-1)[/tex]
substitute
[tex]y+1=-(1)(x-2)[/tex]
[tex]y+1=-(x-2)[/tex]
step 3
Convert to slope intercept form
[tex]y=mx+b[/tex]
isolate the variable y
[tex]y+1=-x+2[/tex]
[tex]y=-x+2-1[/tex]
[tex]y=-x+1[/tex]
