Question

In the following problems, find the slope of a line that is perpendicular to the given lines. (Be sure to express the equation in s intercept form first.) 1. 12x-3y=9

Answer 1

The given equation is

`12x-3y=9`

First, we have to isolate y to find the slope.

`\begin{gathered} -3y=9-12x \\ y=(9-12x)/(-3) \\ y=4x-3 \end{gathered}`

Remember that the slope is the coefficient of x. The slope of the given line is 4.

Then, we use the formula for the perpendicular slope to find the new one.

`\begin{gathered} m\cdot m_1=-1 \\ m\cdot4=-1 \\ m=-(1)/(4) \end{gathered}`

The slope of the new perpendicular line is -1/4.