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

Question

Quizplus · Accepted Answer

The slope of the line $9x - 5y = 108$ is $\frac{9}{5}$. A line perpendicular to it will have a slope of $-\frac{5}{9}$. Using the point-slope form $y - y_1 = m(x - x_1)$ with $m = -\frac{5}{9}$ and $(x_1, y_1) = (7, 9)$, we get $y - 9 = -\frac{5}{9}(x - 7)$. Simplifying and converting to standard form $Ax + By = C$, we get $5x + 9y = 116$.

Find an Equation for the Line with the Given Properties 9x−5y=1089 x - 5 y = 1089x−5y=108

Find an Equation for the Line with the Given Properties $9 x - 5 y = 108$