Question

Write an equation of the straight line which is perpendicular

to the line 2x – 3y = 5 at the point (4,1).

Answer 1

3x + 2y = 14

Explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Rearrange 2x - 3y = 5 into this form by subtracting 2x from both sides

- 3y = - 2x + 5 ( divide all terms by - 3 )

y =
`(2)/(3)` x -
`(5)/(3)` ← in slope- intercept form

with slope m =
`(2)/(3)`

Given a line with slope m then the slope of a line perpendicular to it is

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/((2)/(3) )` = -
`(3)/(2)` , thus

y = -
`(3)/(2)` x + c ← is the partial equation

To find c substitute (4, 1) into the partial equation

1 = - 6 + c ⇒ c = 1 + 6 = 7

y = -
`(3)/(2)` x + 7 ← in slope- intercept form

Multiply through by 2

2y = - 3x + 14 ( add 3x to both sides )

3x + 2y = 14 ← in standard form