Question

find the equation of the line passing through the origin and parallel perpendicular to the line 6x -11y +5=0​

Answer 1

Answer:

6x-11y+5=0

6x=0

x=0/6

for origin

-11y=-5

11y=5

y=5/11

Answer 2

Answer:

Parallel

$6x - 11y + 5 = 0 \\ 11y = 6x + 8 \\ \\ y = \frac{6}{11} x + \frac{8}{11}$

Compare with

$y = mx + c$

Slope = 6/11

So equation of parallel to line

$y = \frac{6}{11} x + c$

c = 0 , Since it pass through origin ( Satisfy (0,0) )

$y = \frac{6}{11} x + 0 \\ \\ 11y = 6x \\ 6x - 11y = 0$

Perpendicular

Let slope of perpendicular line m then

$m( \frac{6}{11} ) = - 1 \implies \: m = \frac{ - 11}{6}$

So line of equation

$y = \frac{ - 11}{6} x + c \: \\ c = 0 \\ \\ 6y = - 11x \\ 11x + 6y = 0$