The equation of the line that is perpendicular to the line 3y - 4x = 6 is: c. 4y + 3x = 8.
<h3>How to Determine the Equation of Lines that are Perpendicular?</h3>
The lines that are perpendicular to each other have slope value of their equation, m, that are negative reciprocals of each other or the product of their slopes is equal to -1.
Given the line 3y - 4x = 6, rewrite the equation in slope-intercept form, y = mx + b, and determine the value of m:
3y = 4x + 6
Divide both sides by 3
3y/3 = 4x/3 + 6/3
y = 4/3x + 2
The slope (m) = 4/3.
The slope of the line that would be perpendicular to the line 3y - 4x = 6, will have a slope of -3/4, which is the negative reciprocal of 4/3.
Rewrite 4y + 3x = 8 in slope-intercept form:
4y = -3x + 8
4y/4 = -3/4x + 8/4
y = -3/4x + 2
The slope of 4y + 3x = 8 is -3/4.
Therefore, the perpendicular line is: c. 4y + 3x = 8.
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