Question

Please help me do this question I have a test soon!

Answer 1

2x + 3y - 4 = 0

Explanation:

Equation of the line → 2x - 3y + 4 = 0

3y = 2x + 4

y =
`(2)/(3)x+(4)/(3)`

Slope of this line 'm' =
`(2)/(3)`

y-intercept of this line → y =
`(4)/(3)` Or
`(0, (4)/(3))`

Let the equation of the line is,

y = m'x + b'

By the property of perpendicular lines,

m × m' = -1

`(2)/(3)* m'=-1`

m' =
`-(3)/(2)`

Equation of the perpendicular line will be,

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

Since this line passes through
`(0, (4)/(3))`,

`(4)/(3)=-(3)/(2)* 0+b'`

b' =
`(4)/(3)`

Therefore, equation of the perpendicular line will be,

y =
`-(2)/(3)x+(4)/(3)`

3y = -2x + 4

2x + 3y - 4 = 0