Question

Find the equation of the line which is parallel to 3x − 2y = −4 and passes through the point (0, 3).

Answer 1

⇒ Rewriting the given equation 3x − 2y = −4 into the slope-intercept form, y = mx + c to find the slope (m₁):

−2y = −3x − 4

`y = (-3)/-2 x - 4/-2`

`y = 3/2 x + 2`

∴ m₁ = `3/2`

⇒ Since the required line is parallel to the given line, their slopes are equal:

`m_2 = m_1 = 3/2`

⇒ Using the slope-intercept form y = mx + c:

`y = 3/2 x + 3`

2y = 3x + 6    ...[Multiplied equation by 2.]

⇒ Rearranging the above equation in the standard form (Ax + By + C = 0),

3x − 2y + 6 = 0

Hence, the equation of the line is 3x − 2y + 6 = 0.