2014-05-12 09:00:11

y = -x/2 + 2

Which of the following is an equation of a line that is perpendicular to the line above and passes through the point (3,1)?

(A) y = 2x - 5
(B) y = -2x - 5
(C)  y = 2x + 3
(D) y = -x/2 - 3
(E)  y = -x/2 + 2.5

The correct answer is A
Explanation: Perpendicular lines have slopes that are negative reciprocals of each other. Thus, to be perpendicular to -x/2, the slope of the new line would have to be 2x, as 2 is positive, unlike -x/2, and as 2 is the reciprocal of x/2. To find the y-intercept, plug in the two points listed for x and y in the equation y = 2x + b:

1 = 2(3) + b

1 = 6 + b

Subtract 6 from both sides to get b = -5.  Thus, the equation of the line is y = 2x - 5