Write an equation of the line. Write the equation in the form x = a, y = b, or y = mx + b.
-Through (-6,8) ; perpendicular to 9 x+5y=66
A) $y = - \frac { 9 } { 5 } x + 66$
B) $y = - \frac { 9 } { 5 } x + 8$
C) $y = \frac { 5 } { 9 } x + \frac { 34 } { 3 }$
D) $y = - \frac { 5 } { 9 } x + \frac { 34 } { 3 }$

Question

Write an equation of the line. Write the equation in the form x = a, y = b, or y = mx + b.
-Through  (-6,8) ; perpendicular to  9 x+5y=66 
A) $y = - \frac { 9 } { 5 } x + 66$
B) $y = - \frac { 9 } { 5 } x + 8$
C) $y = \frac { 5 } { 9 } x + \frac { 34 } { 3 }$
D) $y = - \frac { 5 } { 9 } x + \frac { 34 } { 3 }$

Quizplus · Accepted Answer

The slope of the line perpendicular to $9x + 5y = 66$ is the negative reciprocal of the slope of $9x + 5y = 66$. The slope of $9x + 5y = 66$ is $-\frac{9}{5}$, so the perpendicular slope is $\frac{5}{9}$. Using the point $(-6,8)$ and the slope $\frac{5}{9}$, we use the point-slope form $y - y_1 = m(x - x_1)$ to get $y - 8 = \frac{5}{9}(x + 6)$, which simplifies to $y = \frac{5}{9}x + \frac{34}{3}$.

Write an Equation of the Line y=−95x+66y = - \frac { 9 } { 5 } x + 66y=−59​x+66

Write an Equation of the Line $y = - \frac { 9 } { 5 } x + 66$