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        

$y= \frac{4}{9}x-2$

passes through the line (4,3 )

Find out the equation of the perpendicular line.

To proof

given equation is

 $y= \frac{4}{9}x-2$

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

$m =\frac{4}{9}$

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

= $\frac{-9}{4}$

Than equation perpendicular line becomes

$y= \frac{-9}{4}x + c$

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

put these value in the above equation

we get

$3= \frac{-9}{4}\times 4 + c$

solving the above equation

3 +9 =c

12 =c

put this value in the above equation

we get

$y= \frac{-9}{4}\times x + 12$

this is equation of the perpendicular line.

Hence proved