# What is the equation of the line perpendicular to y=-5/7x  that passes through  (1,-4) ?

Jan 21, 2016

$5 y = 7 x - 27$

#### Explanation:

If a line has slope $m$ then the line perpendicular to it has slope $- \frac{1}{m}$.
Therefore the slope of the line perpendicular to $y = - \frac{5}{7} \cdot x$ has slope $\frac{7}{5}$.
Using the general equation of a straight line $y = m x + c$ and the coordinates of the given point, we have
$- 4 = \left(\frac{7}{5}\right) \left(1\right) + c$
$- 4 - \frac{7}{5} = c$
$c = - \frac{27}{5}$
The equation of the line is therefore $y = \frac{7}{5} \cdot x - \frac{27}{5}$ or

$5 y = 7 x - 27$