# 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, }y_{1}) and (x_{2} , y_{2}) is given by y - y_{1} = m (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 - 1 = m ( x - (-1) ) -------(1)

m = (y_{2} - y_{1}) / (x_{2} - x_{1})

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.

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