Answer:
[tex]y=-\frac{3}{5}x+\frac{7}{5}[/tex]
Step-by-step explanation:
The correct question is
Write an equation for the line passing through (-6,5) and (4,-1)
step 1
Find the slope
we know that
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
we have
(-6,5) and (4,-1)
substitute
[tex]m=\frac{-1-5}{4+6}[/tex]
[tex]m=\frac{-6}{10}[/tex]
[tex]m=-\frac{3}{5}[/tex]
step 2
Find the equation of the line in point slope form
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=-\frac{3}{5}[/tex]
[tex]point\ (-6,5)[/tex]
substitute
[tex]y-5=-\frac{3}{5}(x+6)[/tex]
step 3
Convert to slope intercept form
[tex]y=mx+b[/tex]
Isolate the variable y
[tex]y-5=-\frac{3}{5}x-\frac{18}{5}[/tex]
[tex]y=-\frac{3}{5}x-\frac{18}{5}+5[/tex]
[tex]y=-\frac{3}{5}x+\frac{7}{5}[/tex]