How do you write an equation of a line that passes through points (-1, 3), (2, -3)?

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 (-1, 3) and (2, -3) is 2x +y = + 1.

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

Explanation:

Let us consider the given points (-1,3) and (2,-3).

As we know that the equation of a line passing through the points (x_1, 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)

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 - 1 = m ( x - (-1) ) -------(1)

m =  (y₂ - y₁) / (x₂ - x₁)

m = (-3 - 3) / (2 - (-1))

m = -6 / 3 = -2

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

y - 3 = -2 ( x + 1)

y - 3 = -2x - 2

y = -2x + 1

2x + y = 1

Therefore, the equation of a line passing through the points (-1, 3) and (2, -3) is 2x + y = + 1.