Answer:
The correct option is D
The line perpendicular to the given line is:
3x + 4y = 6
Step-by-step explanation:
Given the line:
4x + 3y = 9
This can be written as:
y = (-4/3)x + 3
This has slope -4/3, and y-intercept 3, a line perpendicular to this has it's slope as: -3/4. Let the line be:
y = (-3/4)x + b
Using the given points (-2, 3), we can obtain the y-intercept.
Using x = -2 and y = 3, we have:
3 = (-3/4)(-2) + b
3 = 3/2 + b
b = 3 - (3/2)
= 3/2
Therefore, the line is:
y = (-3/4)x + 3/2
Multiply through by 4, we have:
4y = -3x + 6
3x + 4y = 6