Question

Equation through (-1,4) and perpendicular to 3y=2x-1

Answer 1

The equation of line perpendicular to given line and passes through points ( - 1 , 4 ) is 2y = -3x + 5

Explanation:

Given line equation as :

3 y = 2 x - 1

Or, y =
`(2)/(3)` x -
`(1)/(3)`

So , The equation is in the form of y = m x + c

Where m is the slope of the line

∴ satisfying the condition

Slope of given line is m =
`(2)/(3)`

Now , ∵ The other line is perpendicular to this line and passes through point ( - 1 , 4 )

Let , Slope of other line = M

∴ for perpendicular line condition , products of the slope = - 1

I.e m × M = - 1

Or , M = -
`(1)/(m)`

Or M = -
`(1)/((2)/(3))`

Or M = -
`(3)/(2)`

Thus The equation of line with slope M and passing through points ( - 1 , 4 ) is

`y-y_1 = M (x-x_1)`

or,
`y-4 = - [tex](3)/(2)` (x + 1)[/tex]

or, 2y - 8 = - 3 (x +1)

Or, 2y - 8 = - 3x - 3

or 2y = - 3x - 3 + 8

∴ 2y = -3x + 5

Hence The equation of line perpendicular to given line and passes through points ( - 1 , 4 ) is 2y = -3x + 5 Answer