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

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

Step-by-step explanation:

Given line equation as :

3 y = 2 x - 1

Or, y = x -  

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 =

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 = -

Or   M = -

Or   M =  -

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

or,   (x + 1)" alt="\frac{3}{2}" />   (x + 1)" />

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

2x + 8

step-by-step explanation: