# How do you find the slope that is perpendicular to the line 3x-9y=15?

Jul 29, 2016

The slope of the line perpendicular to line $3 x - 9 y = 15$ is $- 3$

#### Explanation:

When using the equation of a line, one calculates the value of $y$ in terms of $x$, say $y = m x + c$, then $m$ is the slope of the line and $c$ is its intercept on $y$-axis.

As $3 x - 9 y = 15$ can be written as $3 x - 15 = 9 y$ or

$y = \frac{3}{9} x - \frac{15}{9}$ or $y = \frac{1}{3} x - \frac{5}{3}$

Hence slope of $3 x - 9 y = 15$ is $\frac{1}{3}$

Product of slopes of two perpendicular lines is $- 1$

Hence, the slope of the line that is perpendicular to the line $3 x - 9 y = 15$ is $- \frac{1}{\frac{1}{3}} = - 1 \times \frac{3}{1} = - 3$

graph{(3x-9y-15)(3x+y+5)=0 [-10, 10, -7.04, 2.96]}