# How to find the equation of a line when given two points?

Straight lines are a very important topic one must understand in order to do well in coordinate geometry. They are used to graphically represent linear equations and fin their applications in various fields related to engineering and science. For understanding them, we first need to understand how an equation is represented by a straight line.

## Answer: If two points: (x_{1,}y_{1}) and (x_{2}, y_{2) }are given, then the equation of the line having these two points is: y - y_{1}= m (x - x_{1}); where m = (y_{2}_{ }- y_{1})/(x_{2} - x_{1})

Let's have a look at the explanation of the problem.

**Explanation:**

Let's assume the two points to be (x_{1}, y_{1}) and (x_{2}, y_{2}).

To find the equation of a given straight line, we first need to know its slope.

Hence, we know that slope is given by perpendicular/base.

Therefore, slope (m) = (y_{2}_{ }- y_{1}) / (x_{2} - x_{1}).-------( 1)

After that, we use the point-slope form to arrive at the final solution.

Therefore, using y - y_{1} = m (x - x_{1}), we get: y - y_{1} = (y_{2}_{ }- y_{1})(x - x_{1}) / (x_{2} - x_{1}). [ from equation 1 ]

### Hence, If two points: (x_{1}, y_{1}) and (x_{2}, y_{2}) are given, then the equation of the line having these two points is: y - y_{1 }= m (x - x_{1}); where m = (y_{2}- y_{1}) / (x_{2} - x_{1}).

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