Question

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

Answer 1

Answer:

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 = $\frac{2}{3}$ x -  $\frac{1}{3}$

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 = $\frac{2}{3}$

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 = - $\frac{1}{m}$

Or   M = - $\frac{1}{\frac{2}{3}}$

Or   M =  - $\frac{3}{2}$

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

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

or, $y-4 = - [tex]\frac{3}{2}$   (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