Algebra-1

To determine which equation is perpendicular to 4x - 3y = 8, we need to analyze the slopes of the lines.

The given equation can be rearranged into the slope-intercept form (y = mx + b), where m is the slope:

4x - 3y = 8
-3y = -4x + 8
y = (4/3)x - 8/3

The slope of the given line is 4/3. Any line perpendicular to this line will have a slope that is the negative reciprocal of 4/3, which is -3/4.

Let's analyze the options:

A. -4x - 3y = 8
To determine the slope of this equation, we rearrange it into the slope-intercept form:
-3y = 4x + 8
y = (-4/3)x - 8/3

The slope of this line is -4/3, not the negative reciprocal of 4/3. Therefore, equation A is not perpendicular to 4x - 3y = 8.

B. 6x + 8y = 9
To determine the slope of this equation, we rearrange it into the slope-intercept form:
8y = -6x + 9