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:
[tex]4x-y=9[/tex]Subtract 4x from both sides:
[tex]\begin{gathered} 4x-4x-y=-4x+9 \\ \\ -y=-4x+9 \end{gathered}[/tex]Divide all terms by -1:
[tex]\begin{gathered} \frac{-y}{-1}=\frac{-4x}{-1}+\frac{9}{-1} \\ \\ y=4x-9 \end{gathered}[/tex]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
[tex]\begin{gathered} m_1m_2=-1 \\ \\ m_2=\frac{-1}{m_1} \\ \\ m_2=\frac{-1}{4} \\ \\ m_2=-\frac{1}{4} \end{gathered}[/tex]Therefore, the slope of the perpendicular line is:
[tex]-\frac{1}{4}[/tex]ANSWER:
[tex]-\frac{1}{4}[/tex]