Question

Line l passes through (1,-3) and i perpendicular to `y=1/5x-7` What the equation of line l?

Answer 1

The slope of the perpendicular is the negative reciprocal of the slope of the given line, and the constant is determined by the point it passes through, giving #y =-5x+2. #

Explanation:

The usual method is to say the slope is `1/5` so the slope of the perpendicular is the negative reciprocal `-5` so `y=-5x + b` means `-3 = -5(1) + b` or `b=2` so `y =-5x+2`.

My preferred method is to bring `x` and `y` to the same side, `y - 1/5 x = -7` then swap the coefficients on `x` and `y`, negating one of them, and set the constant to fit: `1/5 y +x = (1/5) (-3) + 1 = 2/5` or multiplying through, `y + 5x = 2.`