Question

Find the equations of the line that passes trough point (3,4)and is perpendicular to the given line. 3x+2y=4

Answer 1

The point is given (3,4) and the line is given 3x+2y=4 which is perpendicular to the equation of line determined.

Then slope of the equation line is

$m=\frac{-1}{slope\text{ of perpendicular line}}$

The slope of perpendicular line is

$y=-\frac{3}{2}x+2$

slope is -3/2.

Then the slope od equation of line is

$m=-\frac{1}{-\frac{3}{2}}=\frac{2}{3}$

Then the equation of line obtained is

$y=mx+c$$4=\frac{2}{3}\times3+c$$4-2=c\text{.}$$c=2$

The equation of line formed is

$y=\frac{2}{3}x+2$