Line p is defined by 4 y + 8 x = 6 . Line r is perpendicular to line p

Question

Line p is defined by 4 y + 8 x = 6 . Line r is perpendicular to line p in the xy -plane. What is the slope of line r ?

Accepted Answer

The correct answer is 1 2 . 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 p is defined by 4 y + 8 x = 6 . Subtracting 8 x from both sides of this equation yields 4 y = - 8 x + 6 . Dividing both sides of this equation by 4 yields y = - 8 4 x + 6 4 , or y = - 2 x + 3 2 . Thus, the slope of line p is - 2 . If line r is perpendicular to line p , then the slope of line r is the negative reciprocal of the slope of line p . The negative reciprocal of - 2 is - 1 - 2 = 1 2 . Note that 1/2 and .5 are examples of ways to enter a correct answer.

Question line-p