    # Straight Line Through Two Points ### THEOREM:

To find the equation of a straight line which passes through the two given points (x1, y1) and (x2, y2).

Solution: < br>
We know that the equation of a straight line is y = mx + c                      (1)

If the straight line represented by equation (1) passes through the point (x1, y1) then,

y1 = m x1 + c                      (2)

or c = y1 - m x1

Now putting the value of c = y1 - m x1 in equation (1) we get,

y = mx + y1 - m x1

or y - y1 = m(x - x1)                       (3)

This is the equation of the line going through (x1, y1) making an angle tan-1 m with OX. If equation (3) passes through the point (x2, y2) then,

y2 - y1 = m(x2 - x1)

or m = Putting the value of m in equation(3) we get,

y - y1 = (x - x1)           which is the required equation.

Example:

Find the equation of a straight line which passes through the points (3, 4) and (5, 6).

Solution:

We know that the equation of a straight line passing through two points is,

y - y1 = (x - x1)

Here the two points are (3, 4) and (5, 6) hence the equation becomes,

y � 4 = (x � 3)

y � 4 = (x � 3)

or y � 4 = x � 3

or y � x = 1               (Answer)

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