Find an equation of the line satisfying the conditions. Write the equation in the form x = a, y = b, or y = mx + b.
-Through (-9,-2) ; perpendicular to 7 x+6 y=75
A) $y = - \frac { 7 } { 6 } x + 75$
B) $y = \frac { 6 } { 7 } x + \frac { 40 } { 7 }$
C) $y = - \frac { 7 } { 6 } x - 2$
D) $y = - \frac { 6 } { 7 } x + \frac { 40 } { 7 }$

Question

Find an equation of the line satisfying the conditions. Write the equation in the form x = a, y = b, or y = mx + b.
-Through  (-9,-2) ; perpendicular to  7 x+6 y=75 
A) $y = - \frac { 7 } { 6 } x + 75$
B) $y = \frac { 6 } { 7 } x + \frac { 40 } { 7 }$
C) $y = - \frac { 7 } { 6 } x - 2$
D) $y = - \frac { 6 } { 7 } x + \frac { 40 } { 7 }$

Quizplus · Accepted Answer

The slope of the line perpendicular to $7x + 6y = 75$ is $-\frac{7}{6}$ (the negative reciprocal of the original slope, which is $\frac{7}{6}$). Using the point (-9, -2) to solve for $b$ in $y = mx + b$, we get $b = \frac{40}{7}$, making the correct equation $y = \frac{6}{7}x + \frac{40}{7}$.

Find an Equation of the Line Satisfying the Conditions y=−76x+75y = - \frac { 7 } { 6 } x + 75y=−67​x+75

Find an Equation of the Line Satisfying the Conditions $y = - \frac { 7 } { 6 } x + 75$