Question

What is the equation of the line perpendicular to the line y=4/9x-2 that passes through the line 4,3

Answer 1

Y=-9/4x-3 (the slope to a perpendicular pair is the reciprocal of the opposite)

Answer 2

Given

The line equation is

`y= (4)/(9)x-2`

passes through the line (4,3 )

Find out the equation of the perpendicular line.

To proof

given equation is

`y= (4)/(9)x-2`

the equation of line is in the form y = mx +c

where m = slope

c is the intercept on the y axis.

compare this equation to the above equation

we get

`m =(4)/(9)`

In perpendicular line case

The slope of a perpendicular line is the "negative reciprocal" of the slope of the original line.

thus slope of the perpendicular line

=
`(-9)/(4)`

Than equation perpendicular line becomes

`y= (-9)/(4)x + c`

as the line passes through the point( 4,3)

put these value in the above equation

we get

`3= (-9)/(4)* 4 + c`

solving the above equation

3 +9 =c

12 =c

put this value in the above equation

we get

`y= (-9)/(4)* x + 12`

this is equation of the perpendicular line.

Hence proved