2012-04-11 09:00:28

Which of the following is the equation for a line that passes through the point (0,3) and that is perpendicular to the line 3x - y = 6?

(A) 3x + 3
(B) -⅓ - 6
(C) ⅓x - 6
(D) 3x - 6
(E) -⅓x + 3

The correct answer is E

Explanation: Start by rewriting 3x - y = 6 in slope-intercept (y = mx + b) form by solving the equation for y. Add y to both sides, leaving 3x = 6 + y, then subtract 6 from both sides to isolate the y, leaving the line 3x - 6 = y.  Perpendicular lines have negative reciprocal slopes, so a line that is perpendicular to 3x - 6 = y would have a slope that is the negative reciprocal of 3x. The negative reciprocal of 3x would be -⅓x. The y-intercept of this line is given in the prompt, as the point (0,3) is the y-intercept, meaning the b part of this equation is 3. Thus, the correct line is the one given in choice E: -⅓x + 3.