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

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.
The usual method is to say the slope is $\frac{1}{5}$ so the slope of the perpendicular is the negative reciprocal $- 5$ so $y = - 5 x + b$ means $- 3 = - 5 \left(1\right) + b$ or $b = 2$ so $y = - 5 x + 2$.
My preferred method is to bring $x$ and $y$ to the same side, $y - \frac{1}{5} x = - 7$ then swap the coefficients on $x$ and $y$, negating one of them, and set the constant to fit: $\frac{1}{5} y + x = \left(\frac{1}{5}\right) \left(- 3\right) + 1 = \frac{2}{5}$ or multiplying through, $y + 5 x = 2.$