Question

two lines a and b are perpendicular. line a has equation 3y-2x+2=0 and meets line b at the point(4,7). find the equation of line b

Answer 1

Answer:

Step-by-step explanation:

3y - 2x +2 = 0

3y = 2x - 2

$y = \dfrac{2}{3}x-\dfrac{2}{3}$

y = mx + b

Slope of line a = 2/3

Product of slope of perpendicular line = -1

$Slope \ of \ line \ b = \dfrac{-1}{\dfrac{2}{3}}=\dfrac{-3}{2}$

Equation of line b:

$y=\dfrac{-3}{2}x+b$

Line b passes through (4,7)

$7 = \dfrac{-3}{2}*4+b\\\\\\7= -6 + b\\\\b = 7 + 6\\\\b = 13$

Equation of line b:

$y=\dfrac{-3}{2}x+13$

Multiply the  equation by 2

2y = -3x + 26

3x + 2y - 26 = 0