Answer:
[tex]y=-2x[/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
(-5,10) and (5,-10)
substitute the values in the formula
[tex]m=\frac{-10-10}{5+5}[/tex]
[tex]m=\frac{-20}{10}[/tex]
[tex]m=-2[/tex]
step 2
Find the equation in point slope form
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=-2[/tex]
[tex]point\ (5,-10)[/tex]
substitute
[tex]y+10=-2(x-5)[/tex]
step 3
Convert to slope intercept form
[tex]y=mx+b[/tex]
isolate the variable y
apply distributive property right side
[tex]y+10=-2x+10[/tex]
[tex]y=-2x[/tex]
