# Find the equation of the line passing through points (1,1) and (4,-12)?

We will be using the concept of the equation of a line passing through two points to solve this question.

## Answer: The equation of line passing through points (1,1) and (4,-12) is y = (-13x + 16)/3

Let's solve this step by step.

**Explanation: **

Given that, (x_{1}, y_{1}) = (1,1) and (x_{2}, y_{2}) = (4,-12)

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})

Substitute the given point (x_{1}, y_{1}) = (1,1) in the equation of a line,

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

Also, (x_{2}, y_{2}) = (4,-12)

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

m = (-12 - 1) / (4 - 1)

m = -13 / 3

Substituting value of m in (1), we get

⇒ y - 1 = (-13 / 3) (x - 1)

⇒ 3y - 3 = -13x + 13

⇒ 3y = -13x + 16

⇒ y = (-13x + 16) / 3

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