Find the equation of a line passing through the point (2, 3) and intersecting the line 2x – 3y = 6 on the y-axis.

On the y-axis,

x = 0.

Substitute x = 0 into 2x − 3y = 6:

⇒ 2(0) − 3y = 6

⇒ −3y = 6

⇒ y = −2

So, the line 2x − 3y = 6 meets the y-axis at (0, -2).

Calculating slope for points (2, 3) and (0, -2).

By formula,

Slope = $\dfrac{y$2 - y1}{x2 - x1}

m = $\dfrac{3 -(-2)}{2 - 0} = \dfrac{5}{2}$

By two-point form :

Equation of a line :

y - y₁ = m(x - x₁)

Substituting values we get :

⇒ y - (-2) = $\dfrac{5}{2}$ (x - 0)

⇒ 2(y + 2) = 5x

⇒ 2y + 4 = 5x

⇒ 5x - 2y - 4 = 0

Hence, equation of line 5x - 2y = 4.