Line l is defined by 3 y + 12 x = 5 . Line n is perpendicular to line l

Question

Line l is defined by 3 y + 12 x = 5 . Line n is perpendicular to line l in the xy -plane. What is the slope of line n ?

Accepted Answer

The correct answer is 1 4 . For an equation in slope-intercept form y = m x + b , m represents the slope of the line in the xy -plane defined by this equation. It's given that line l is defined by 3 y + 12 x = 5 . Subtracting 12 x from both sides of this equation yields 3 y = - 12 x + 5 . Dividing both sides of this equation by 3 yields y = - 12 3 x + 5 3 , or y = - 4 x + 5 3 . Thus, the slope of line l in the xy -plane is - 4 . Since line n is perpendicular to line l in the xy -plane, the slope of line n is the negative reciprocal of the slope of line l . The negative reciprocal of - 4 is - 1 - 4 = 1 4 . Note that 1/4 and .25 are examples of ways to enter a correct answer.

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