The Solution:
Given:
[tex]y=4x+5[/tex]Required:
Find the equation of the line that passes the point (8,-4) and it is perpendicular to y = 4x + 5.
Step 1:
Find the slope of y = 4x+5.
Comparing the line y = 4x +5 and y = mx + c.
The slope of the line is:
[tex]slope=m=4[/tex]Thus, for a line that is perpendicular to y = 4x + 5, the slope is:
[tex]slope=m_2=\frac{-1}{m}=\frac{-1}{4}[/tex]Step 2:
Find the required equation of the perpendicular line.
[tex]\begin{gathered} y-y_1=m_2(x-x_1) \\ \\ x_1=8 \\ y_1=-4 \end{gathered}[/tex]Substitute:
[tex]\begin{gathered} y--4=\frac{-1}{4}(x-8) \\ \\ y+4=\frac{-1}{4}(x-8) \\ \\ y=-\frac{1}{4}x+2-4 \\ \\ y=-\frac{1}{4}x-2 \end{gathered}[/tex]Answer:
[tex]y=-\frac{1}{4}x-2[/tex]
