Answer:
Option A: [tex]-\frac{4}{3}[/tex] is the correct answer.
Step-by-step explanation:
Given that:
Slope of the line = [tex]\frac{3}{4}[/tex]
Let,
m be the slope of the line perpendicular to the line with slope [tex]\frac{3}{4}[/tex]
We know that,
The product of slopes of two perpendicular lines is equals to -1.
Therefore,
[tex]\frac{3}{4}.m=-1\\[/tex]
Multiplying both sides by [tex]\frac{4}{3}[/tex]
[tex]\frac{4}{3}*\frac{3}{4}m=-1*\frac{4}{3}\\[/tex]
m = [tex]-\frac{4}{3}[/tex]
[tex]-\frac{4}{3}[/tex] is the slope of the line perpendicular to the line having slope [tex]\frac{3}{4}[/tex]
Hence,
Option A: [tex]-\frac{4}{3}[/tex] is the correct answer.
