Question

What is the slope of a line perpendicular to the line whose equation is 4x - y = 9.Fully simplfy

Answer 1

Given the equation of the original line:

4x - y = 9

Let's find the slope of a line perpendicular to the original line.

The slope of a perpendicular line is the negative reciprocal of the slope of the original line.

Let's find the slope of the original line.

Apply the slope-intercept form of a linear equation:

y = mx + b

Where m is the slope.

We have:

$4x-y=9$

Subtract 4x from both sides:

$\begin{gathered} 4x-4x-y=-4x+9 \\ \\ -y=-4x+9 \end{gathered}$

Divide all terms by -1:

$\begin{gathered} \frac{-y}{-1}=\frac{-4x}{-1}+\frac{9}{-1} \\ \\ y=4x-9 \end{gathered}$

Thus, the equation of the original line in slope-intercept form is:

y = 4x - 9

The slope of the original line is = 4

The slope of the perpendicular line will be the nagative reciprocal of the slope of the original line.

Thus, we have:

Let m1 be the slope of the original line

Let m2 be the slope of the perpendicular line

$\begin{gathered} m_1m_2=-1 \\ \\ m_2=\frac{-1}{m_1} \\ \\ m_2=\frac{-1}{4} \\ \\ m_2=-\frac{1}{4} \end{gathered}$

Therefore, the slope of the perpendicular line is:

$-\frac{1}{4}$

ANSWER:

$-\frac{1}{4}$