Question

LINE PERPENDICULAR TO Y=1/5X+5 WITH THE POINT (-6,0)?????

Answer 1

You need to flip the slope (or number in front of the x) and sign of it to do the perpendicular part. This should give you: y=-5x+b. Now put the -6 in for the x, and the 0 in for the y. Simply solve for an answer of -30=b. Your final answer is: y=-5x-30

Answer 2

y=1/5x+5 with the point (-6, 0)

The line perpendicular to this line will have a slope that's the negative reciprocal of this one. So if the slope here is 1/5 (based on y=mx+b, where m is the slope), then the perpendicular slope would be -5/1.

So now that you have the point and the slope, use the point-slope formula.
y - y₁ = m(x - x₁)
m = -5
(x₁, y₁) = (-6, 0)

y - 0 = -5(x + 6)
y = -5x - 30

y = -5x - 30 is the line perpendicular to y=1/5x+5.