Find the slope-intercept form of the equation of a line parallel or perpendicular to the given line and passing through the given point.
-Perpendicular to $5 x-9 y=64$, through $(2,6)$
A) $y=-\frac{5}{9} x-\frac{5}{9}$

B) $y=-\frac{9}{5} x+\frac{48}{5}$

C) $y=\frac{9}{5} x+\frac{48}{5}$

D) $y=-\frac{2}{9} x+\frac{64}{9}$

Question

Find the slope-intercept form of the equation of a line parallel or perpendicular to the given line and passing through the given point.
-Perpendicular to $5 x-9 y=64$, through $(2,6)$
A) $y=-\frac{5}{9} x-\frac{5}{9}$

B) $y=-\frac{9}{5} x+\frac{48}{5}$

C) $y=\frac{9}{5} x+\frac{48}{5}$

D) $y=-\frac{2}{9} x+\frac{64}{9}$

Quizplus · Accepted Answer

The slope of the given line $5x - 9y = 64$ is $\frac{5}{9}$. A line perpendicular to this will have a slope that is the negative reciprocal, which is $-\frac{9}{5}$. Using the point-slope form $y - y_1 = m(x - x_1)$ with $m = -\frac{9}{5}$ and the point $(2, 6)$, we find the equation of the line in slope-intercept form to be $y = -\frac{9}{5}x + \frac{48}{5}$.

Find the Slope-Intercept Form of the Equation of a Line 5x−9y=645 x-9 y=645x−9y=64

Find the Slope-Intercept Form of the Equation of a Line $5 x-9 y=64$