# What is the slope of the line perpendicular to y=4/17x+7 ?

Feb 1, 2016

slope$= - \frac{17}{4}$

#### Explanation:

Recall that when a line is perpendicular to another line, its slope is the negative reciprocal of the slope of the other line.

To find the negative reciprocal:

$1.$ Flip the positions of the numerator and denominator around
$2.$ Multiply the whole fraction by $- 1$.

Note that you can also multiply the whole fraction by $- 1$ first before flipping the positions of the numerator and denominator; either way works.

Thus:

$\frac{4}{17} \textcolor{red}{\Rightarrow} \frac{17}{4} \textcolor{red}{\Rightarrow} - 1 \cdot \frac{17}{4} \textcolor{red}{\Rightarrow} - \frac{17}{4}$

OR

$\frac{4}{17} \textcolor{red}{\Rightarrow} - 1 \cdot \frac{4}{17} \textcolor{red}{\Rightarrow} - \frac{4}{17} \textcolor{red}{\Rightarrow} - \frac{17}{4}$

$\therefore$, the slope of the line perpendicular to $y = \frac{4}{17} x + 7$ is $- \frac{17}{4}$.