Answer:
[tex]y = \frac{-4}{3}x + 5[/tex]
Explanation:
The general form of the linear equation is:
y = mx + c
where m is the slope and c is the y-intercet
For two lines to be parallel:
m₁ × m₂ = -1
Now, for the given line:
[tex]y = \frac{3}{4}x + 5[/tex]
The slope of the given line (m₁) is [tex]\frac{3}{4}[/tex]
Now, we get the slope of the line perpendicular to the given one:
[tex]m_{1}*m_{2} = -1\\\frac{3}{4}*m_{2}=-1 .....> m_{2}=\frac{-4}{3}[/tex]
From the given choices:
The only given option with slope [tex]\frac{-4}{3}[/tex] is [tex]y = \frac{-4}{3}x + 5[/tex]
Hope this helps :)
