Question

What is the slope of a line perpendicular to the line whose equation is x - 3y = -18. Fully reduce your answer.​

Answer 1

Given:

Equation of a line is

$x-3y=-18$

To find:

The slope of the line perpendicular to the given line.

Solution:

The slope of the equation $ax+by=c$ is

$Slope=-\dfrac{a}{b}$

We have,

$x-3y=-18$

Here, a=1, b=-3. So, slope of this line is

$m_1=-\dfrac{1}{-3}$

$m_1=\dfrac{1}{3}$

Product of slopes of two perpendicular lines is -1.

Let slope of perpendicular line is $m_2$.

$m_1\cdot m_2=-1$

$\dfrac{1}{3}\cdot m_2=-1$

$m_2=-3$

Therefore, the slope of the perpendicular line is -3.