Find the value of n so that the line perpendicular to y = (-1/5)x-6 passes through the points (n, -14) and (1,6).

Answer 1

For the line provided, the slope is -1/5. The slope for the line perpendicular to this is the negative reciprocal. This gives us a slope of 5.

The equation for slop is m=(y₂-y₁)/(x₂-x₁)

Plugging values into the equation:

5=(6-(-14))/(1-n) Simplify

5=(6+14)/1-n) Simplify

5=20/(1-n) Multiply both sides by (1-n) to clear the fraction

5(1-n)=20 Distributive property to clear the parenthesis

5-5n=20 Subtract 5 from both sides

5-5n-5=20-5 Simplify

-5n=15 Divide both sides by -5

-5n/-5=15/-3

n=-3