Find the perpendicular line equation of 6x - y = 3 with the line passing through (7, -2)

Question

I just started math back up and I honestly don't know what I'm doing. I've tried going through different websites, but they either say "error" or they just give me the answer without showing me how to do it step-by-step. Please help!

Answer 1

The equation 6x-y=3 is rewritten y = 6x-3

You can see that the slope of the line is 6. The slope of the perpendicular lines is -1/6.

So the equation of the perpendicular line passing through (7,-2) is written

y+2 = -(1/6)(x-7) = -(1/6)x + (7/6) Then y = -(1/6)x +(7/6) -2 = -(1/6)x + (7/6) - (12/6)

or

y = -(1/6)x -(5/6) (The perpendicular line)