Question

Write an equation of a line that is perpendicular to the line 2x-3y+15=0

Answer 1

`y =- (3)/(2) x+1`

Explanation:

The equation of the given straight line is 2x - 3y + 15 = 0.

Now, we can express the equation as 3y = 2x + 15

⇒
`y = (2)/(3) x+ 5` ..........(1)

The equation is in slope-intercept form and the slope is =
`(2)/(3)`

Therefore, the equation of a straight line which is perpendicular to (1) is

`y = -(3)/(2) x+c` {Where c is any constant}

{Since, the product of slopes of two perpendicular straight lines is -1}

Now, putting c = 1, we get the equation as
`y =- (3)/(2) x+1`. (Answer)