# What is the equation of the line perpendicular to y=-1/16x  that passes through  (3,4) ?

Feb 16, 2016

Equation of desired line is $y = 16 x - 44$

#### Explanation:

The equation of line y=−(1/16)x is in slope-intercept form $y = m x + c$, where $m$ is slope and $c$ is intercept on $y$ axis.
Hence its slope is −(1/16).

As product of slopes of two perpendicular lines is $- 1$, slope of line perpendicular to y=−(1/16)x is $16$ and slope-intercept form of the equation of line perpendicular will be $y = 16 x + c$.

As this line passes through (3,4), putting these as $\left(x , y\right)$ in $y = 16 x + c$, we get $4 = 16 \cdot 3 + c$ or $c = 4 - 48 = - 44$.

Hence equation of desired line is $y = 16 x - 44$