Find an equation for the line through P(2, 3) that is perpendicular to the line 3x - y = 4.
A) x + 3y = 11
B) 3x - y = 3
C) 3x + y = 9
D) x - 3y = -7
E) 3x + y = 11

Question

Quizplus · Accepted Answer

The slope of the given line 3x - y = 4 is 3 (since it can be rewritten as y = 3x - 4). A line perpendicular to it will have a slope that is the negative reciprocal of 3, which is -1/3. Using the point-slope form of a line (y - y1 = m(x - x1)) with point P(2, 3) and slope m = -1/3, we get y - 3 = -1/3(x - 2). Simplifying this equation to standard form (Ax + By = C) gives x + 3y = 11.

Find an Equation for the Line Through P(2, 3) That