Write an equation of the line. Write the equation in the form x = a, y = b, or y = mx + b.
-Through (2,3) ; perpendicular to y=3x-4
A) $y = - \frac { 1 } { 3 } x + \frac { 11 } { 3 }$
B) $y = \frac { 1 } { 3 } x + \frac { 11 } { 3 }$
C) $y = 3 x + \frac { 11 } { 3 }$
D) $y = - 3 x + \frac { 11 } { 3 }$

Question

Write an equation of the line. Write the equation in the form x = a, y = b, or y = mx + b.
-Through (2,3) ; perpendicular to  y=3x-4
A) $y = - \frac { 1 } { 3 } x + \frac { 11 } { 3 }$
B) $y = \frac { 1 } { 3 } x + \frac { 11 } { 3 }$
C) $y = 3 x + \frac { 11 } { 3 }$
D) $y = - 3 x + \frac { 11 } { 3 }$

Quizplus · Accepted Answer

The slope of the line perpendicular to $y = 3x - 4$ is the negative reciprocal of 3, which is $-\frac{1}{3}$. Using the point (2,3) to solve for $b$ in $y = mx + b$, we get $3 = -\frac{1}{3}(2) + b$, leading to $b = \frac{11}{3}$. Therefore, the equation is $y = -\frac{1}{3}x + \frac{11}{3}$.

Write an Equation of the Line y=−13x+113y = - \frac { 1 } { 3 } x + \frac { 11 } { 3 }y=−31​x+311​

Write an Equation of the Line $y = - \frac { 1 } { 3 } x + \frac { 11 } { 3 }$