Question

Write the equation of a line that is perpendicular to the given line and that passes through the given point.

-3x - 5y = 17; (6, 3)
y=2x-9
y = 2x - 9
y = -2x - 9
y = 2x + 0

Answer 1

y - 3 = (5/3)(x - 6)

Explanation:

The usual first step is to determine the slope of the given line.

In this case the slope is -3/5.

A line perpendicular to this given line would have a slope of 5/3, which is the negative reciprocal of -3/5.

This new line goes thru (6, 3) and has a slope of 5/3. Thus, the equation of the line in point-slope form is

y - 3 = (5/3)(x - 6)

Double check that you have copied the problem down correctly. The slope of the line represented by -3x - 5y = 17 is neither 2 nor -2; it is -3/5, and so the slope of a line perpendicular to -3x - 5y = 17 is +5/3.