Find an equation for the line with the given properties.
-Perpendicular to the line 9x - 5y = 108; containing the point (7, 9)
A) 9x + 5 = 9
B) 5x + 9y = 116
C) 5x - 9y = 116
D) 7x + 5y = 108

Question

Quizplus · Accepted Answer

The slope of the given line 9x - 5y = 108 is found by rearranging it into slope-intercept form (y = mx + b), which gives -5y = -9x + 108, or y = (9/5)x - 108/5. Thus, the slope of the given line is 9/5. A line perpendicular to this one would have a slope that is the negative reciprocal of 9/5, which is -5/9. Using the point-slope form of a line (y - y1 = m(x - x1)) with the point (7, 9) and the slope -5/9, we get y - 9 = (-5/9)(x - 7). Rearranging this into standard form (Ax + By = C) gives 5x + 9y = 116.

Find an Equation for the Line with the Given Properties