Find an equation of the line passing through the points (2, 3) and (4, 6).

The general equation of a straight line can be written as y = mx + c where m is the slope and c is the y-intercept.

Answer: The equation of a line passing through the points (2, 3) and (4, 6) is 3x - 2y = 0

Let us proceed step by step to find the equation of the line.

Explanation:

Let us consider the given points (2, 3) and (4, 6).

As we know that the equation of a line passing through the points (x₁, y₁) and (x₂, y₂) is given by y - y₁ = m (x - x₁).

Here, m is the slope given by the formula m = (y₂ - y₁) / (x₂ - x₁)

Try using Cuemath's Slope Calculator that helps you to calculate the slope in a few seconds.

Hence on substituting the given points in the equation of a line, we get

y - 3 = m (x - 2)

m =  (y₂ - y₁) / (x₂ - x₁)

m = (6 - 3) / (4 - 2)

m = 3 / 2

Substituting value of m in y - 3 = m (x - 2), we get

⇒ y - 3 = 3 / 2 ( x - 2 )

⇒ 2y - 6 = 3x - 6

⇒ 2y - 3x = 0

⇒ 3x - 2y = 0

You can use Cuemath's online Equation of Line calculator to find the equation of line.

Therefore, the equation of a line passing through the points (2, 3) and (4, 6) is 3x - 2y = 0