The equation of straight line through the intersection of the lines x - 2y = 1 and x + 3y = 2 and parallel to 3x + 2y = 0 is:

Concept:

If the two lines are parallel, then their slopes will be equal.

The "point-slope" form of the equation of a straight line is: y – y1 = m (x – x1)

Here (x1, y1) is point on the line and m is the slope of line.

Calculation:

Given lines are x - 2y = 1 and x + 3y = 2 

x - 2y = 1            .... (1)

x + 3y = 2           ..... (2)

equation (2) - equation (1), we get

⇒ (x + 3y) - (x - 2y) = 2 - 1

⇒ 5y = 1

∴ y = 1/5

Put the value of y in equation (1), we get

x = 7/5

Point of intersection: (x, y) = (x₁, y₁) = 

Let slope of the straight line 3x + 2y = 0 is m₁,

So, slope = m₁ = 

We know that when two lines are parallel, then their slopes will be equal.

∴  slope = m = m₁ = 

Now equation of the line is y – y₁ = m (x – x₁)