Question

Through (1,3) perpendicular to 3x+2y=5

Answer 1

The equation of line passing through points (1 , 3) and perpendicular to given line is y =
`(2)/(3)` x +
`(7)/(3)`

Explanation:

Given as :

The equation of line is 3 x + 2 y = 5

Or , 2 y = - 3 x + 5

Or , y =
`(-3)/(2)` x +
`(5)/(2)`

Another line is passing through point (1 , 3) and perpendicular to given line equation

Now, From standard line equation

i.e y = m x + c

where m is the slope of the line and c is the y-intercept

Now, comparing the given line equation with standard line equation

i.e y =
`(-3)/(2)` x +
`(5)/(2)`

So, The slope of line = m =
`(-3)/(2)`

According to question

Another line is perpendicular to the given line

So, for perpendicular property, The product of the lines = - 1

Let the sloe of another line = M

So, m × M = - 1

∴ M =
`(-1)/(m)`

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

I.e M =
`(2)/(3)`

So, the slope of another line = M =
`(2)/(3)`

Now, equation of line passing through slope M and point (1 , 3)

I.e equation of line in slope-points

So, y -
`y_1` = m ( x -
`x_1` )

or, y - 3 = (
`(2)/(3)`) × ( x - 1 )

Or, 3 × (y - 3) = 2 × (x - 1)

Or, 3 y - 9 = 2 x - 2

Or, 3 y = 2 x - 2 + 9

Or, 3 y = 2 x + 7

∴ y =
`(2)/(3)` x +
`(7)/(3)`

So, The equation = y =
`(2)/(3)` x +
`(7)/(3)`

Hence, The equation of line passing through points (1 , 3) and perpendicular to given line is y =
`(2)/(3)` x +
`(7)/(3)` Answer