Question

Which equation represents a line that is perpendicular to the line y= 4/3x−6?

Option 1: y=− 3/4x+2
Option 2: y=− 4/3x+8
Option 3: y= 3/4x−2
Option 4: y=4/3 x+2

Answer 1

The line represented by the equation y = -3/4x + 2 is perpendicular to the line y = 4/3x - 6, as it has the negative reciprocal slope of -3/4.

Step-by-step explanation:

The equation that represents a line perpendicular to the line y = 4/3x - 6 must have a slope that is the negative reciprocal of 4/3.

Two lines are perpendicular if their slopes are negative reciprocals of each other, meaning the product of their slopes is -1.

Therefore, we are looking for a slope of -3/4 since -3/4 is the negative reciprocal of 4/3.

Reviewing the provided options for the equation of the perpendicular line:

• Option 1: y = -3/4x + 2 - This has a slope of -3/4, which is the negative reciprocal of 4/3.
• Option 2: y = -4/3x + 8 - This has the same slope as the original line, but negative, so it's not perpendicular.
• Option 3: y = 3/4x - 2 - This has a slope of 3/4, not -3/4, so it's not perpendicular.
• Option 4: y = 4/3x + 2 - This has the same slope as the original line, hence it's not perpendicular.

Based on this analysis, only Option 1 (y = -3/4x + 2) represents a line that is perpendicular to the line y = 4/3x - 6.