Question

Find an equation of a line passing through origin and parallel

to 3x − 2y = 1. [GTU-SUMMER-2017]​

Answer 1

$\huge\blue{\boxed{\underline{ANSWER}}}$

GIVEN THAT:-

$&#10152$ A line passing through origin and parallel to 3x − 2y = 1

EXPLANATION:-

Let a point (x,y) on the line and passing through origin (0,0) .

Another equation :-

$&#10230 \: \: 3x - 2y = 1 \\ \\ &#10230 \: \: 2y = 3x - 1 \\ \\ &#10230 \: \: y = \frac{3}{2} x - \frac{1}{2}$

The slope of this equation (m) is 3/2

• The equation passing through origin is parallel to this line , so the slope of both equation is equal .

• Now the slope of the second line is 3/2 which is passing through a point (x,y) and origin

so the equation of the line

$&#10230 \: \: (x - 0) = \frac{3}{2} (y - 0) \\ \\ &#10230 \: \: x = \frac{3}{2} y \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ &#10230 \: \: 2x - 3y = 0 \: \: \: \: \: \: \: \: \: \: \: \: \:$

Answer 2

Answer:

3x -2y = 0

Step-by-step explanation:

Parallel lines have the same slopes and different y-coordinates.

Coordinate of Line are (0,0) 3x-2y+7 = 6

3x + 1 = 2y

3x + 1 = y 2

m = 32

3 /2 3/ 2

(y-y₁) = m ( x-xx₁1)

(9-0) 3 (x-0) = 2

2y = 3x 3x-2y = 0