22. Which of the following lines is perpendicular to the line y = -3/5x+1 A. 5x – 3y = 27
B. 3x + 5y = 10
C. 3x - 5y = 20
D. 5x + 3y = 21

The line 5x – 3y = 27 is perpendicular to the line y = -3/5x+1.

Hence, option A is correct.

Step-by-step explanation:

Given the line

y = -3/5x+1

comparing with the slope-intercept form of the line equation

y = mx+b

so the slope = m = -3/5

We know that a line perpendicular to another line contains a slope that is the negative reciprocal of the slope of the other line, such as:

slope = m = -3/5

perpendicular slope = – 1/(-3/5) = 5/3

Thus, the new line will have the slope = 5/3

Now Checking the line given in option A

5x – 3y = 27

writing the line in the slope-intercept form of the line equation

3y = 5x-27

divide both sides by 3

y = 5/3x - 9

here the slope m = 5/3 which is the negative reciprocal of the slope of the other line y = -3/5x+1.

Therefore, we conclude that the line 5x – 3y = 27 is perpendicular to the line y = -3/5x+1.

Hence, option A is correct.