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

Explanation:

3y - 2x +2 = 0

3y = 2x - 2

`y = (2)/(3)x-(2)/(3)`

y = mx + b

Slope of line a = 2/3

Product of slope of perpendicular line = -1

`Slope \ of \ line \ b = (-1)/((2)/(3))=(-3)/(2)`

Equation of line b:

`y=(-3)/(2)x+b`

Line b passes through (4,7)

`7 = (-3)/(2)*4+b\\\\\\7= -6 + b\\\\b = 7 + 6\\\\b = 13`

Equation of line b:

`y=(-3)/(2)x+13`

Multiply the equation by 2

2y = -3x + 26

3x + 2y - 26 = 0