175,967 views
34 votes
34 votes
Which equation represents the line that is perpendicular to the graphof 4x + 3y = 9 and passes through (-2, 3)?A3x – 4y = -18B3x + 4y = 18C3x - 4y = -6D3x + 4y = 6

User Christophe Chenel
by
3.5k points

1 Answer

26 votes
26 votes
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

User Anthony Ngene
by
2.6k points