Find an equation in slope-intercept form (where possible) for the line.
-Through $ (5,9) $, perpendicular to $ -9 x-4 y=-9 $
A) $ y=\frac{4}{9} x+\frac{61}{9} $
B) $ y=-\frac{5}{4} x-\frac{9}{4} $
C) $ y=-\frac{4}{9} x+\frac{61}{9} $
D) $ y=\frac{9}{4} x+\frac{9}{4} $

Question

Quizplus · Accepted Answer

The slope of the given line is found by rewriting it in slope-intercept form: $y = mx + b$. The given equation is $-9x - 4y = -9$, which can be rewritten as $y = \frac{9}{4}x + \frac{9}{4}$. The slope of this line is $\frac{9}{4}$. The slope of a line perpendicular to this one is the negative reciprocal of $\frac{9}{4}$, which is $-\frac{4}{9}$. Using the point-slope form of a line, $y - y_1 = m(x - x_1)$, with $m = -\frac{4}{9}$ and the point $(5, 9)$, we get $y - 9 = -\frac{4}{9}(x - 5)$. Simplifying this equation to slope-intercept form gives $y = -\frac{4}{9}x + \frac{61}{9}$, which matches choice A.

Find an Equation in Slope-Intercept Form (Where Possible) for the Line