## Equation Of The Line

In this page equation of the line we are going to see how to find the equation of the given line.

We have several ways to find the equation.We have shown four ways.A linear equation or an equation of the first degree in x and y represents a straight line.The equation of a straight line is satisfied by the co-ordinates of every point lying on the straight line and not by any other point outside the straight line.

(i) Slope intercept form:

y = m x + b

Here m = slope and b = y-intercept

If we have slope of the line and the y-intercept we can use this formula to find the equation of a straight line

(ii)  Two point form:

(y-y1)/(y2-y1) = (x-x1)/(x2-x1)

Here (x1,y1) and (x2,y2) are the points on the line.

If we have any two points on the line we can use this formula to find the equation.

(iii) Point- Slope form:

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

Here m = slope and (x1,y1) are the given point on the line.

If we have slope and one point is on the line we can use this formula to find the equation.

(iv) Intercept form:

(X/a) + (Y/b) = 1

Here a = x-intercept and b= y-intercept

If we have x and y intercepts we can use this method to find the equation.

Example 1:

Find the equation of a straight line whose slope is -3 and which passes through the point (-2,3)

Solution:

Slope (m) = -3 and the point (x1,y1) = (-2,3)

Equation of a line:

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

(y - 3) = -3 (x-(-2))

(y-3) = -3 (x + 2)

y - 3 = -3x -6

3x + y +6 -3 = 0

3x + y + 3 =0

Example 2:

Find the equation of the line passing through the points (0,7) and (2,1)

Solution:

Here (x1,y1) = (0,7) and (x2,y2) = (2,1)

Equation of a line:

(y-y1)/(y2-y1) = (x-x1)/(x2-x1)

(y-7)/(2-7) =  (x-0)/(2-0)

(y-7)/(-5) =   x/2

2(y-7) = -5x

2y - 14 = -5x

5x + 2y -14 =0  