Find the equation of a line passing through the points (-1,1) and (2,-4).

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, 1) and (2, -4) is 5x + 3y + 2 = 0.

Let us proceed step by step

Explanation:

Let us consider the given points (-1, 1) and (2, -4).

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).

Where 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 = (-4 - 1) / (2 - (-1))

m = -5 / 3

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

y - 1 = -5 / 3 (x + 1)

3y - 3 = -5 (x + 1)

5x + 3y + 2 = 0

Therefore, the equation of a line passing through the points (-1, 1) and (2, -4) is 5x + 3y + 2 = 0.