What is the equation of the line perpendicular to the line 2x + 3y = -6 and having Y-intercept 3?

Solution (By Examveda Team)

$$\eqalign{ & 2x + 3y = - 6 \cr & y = - \frac{2}{3}x - \frac{6}{3} \cr & \therefore {\text{Slope}} = - \frac{2}{3} \cr} $$
⇒ Two lines are perpendicular if m₁ × m₂ = -1
Y intercept = 3
⇒ y = mx + c
⇒ m₂ = $$\frac{3}{2}$$
The equation of line with slope $$\frac{3}{2}$$ is:-
y - y₁ = m₂(x - x₁)
where, (x₁ y₁) = (0, 3)
y - 3 = $$\frac{3}{2}$$(x - 0)
2y - 6 = 3x
3x - 2y = -6