How to write an equation of the line that passes through the given points?

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 \((x_1, y_1)\) and \((x_2, y_2)\) is \(y - y_1 = [(y_2 - y_1) / (x_2 - x_1)] [ (x - x_1) ]\)

Let us proceed step by step to write an equation of a line.

Explanation:

Let us consider the given points \((x_1, y_1)\) and \((x_2, y_2)\).

As we know that the equation of a line passing through the points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \(y - y_1 = [(y_2 - y_1) / (x_2 - x_1)] [ (x - x_1) ]\).

Here, m is the slope given by the formula m = \((y_2 - y_1) / (x_2 - x_1)\)

You can find the slope using Cuemath's Slope Calculator.

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

\(y - y_1 = m (x - x_1)\)   ------(1)

\(m =  (y_2 - y_1) / (x_2 - x_1)\)

Substituting value of m in equation (1), we get

\(y - y_1 = [(y_2 - y_1) / (x_2 - x_1)] [ (x - x_1) ]\)

Therefore, the equation of a line passing through the points \((x_1, y_1)\) and \((x_2, y_2)\) is \(y - y_1 = [(y_2 - y_1) / (x_2 - x_1)] [ (x - x_1) ]\)