 # Find Equation of a Line

## Equation of line in Point Slope Form

The application below generates two points A and B and the line through them. To find the equation of a line through two points, we first calculate the slope m of the line through the two points given by:
m = (YB - YA) / (XB - XA)

then the equation of the line in
point slope form given by
y - YA = m (x - xA)
or
y - YB = m (x - xB)

.

## Interactive Tutorial with Examples and Solutions

1 - Use the mousse, click press and drag points A and B slowly, determine their coordinates and use the formula of the slope of a line to calculate the slope of the line through the two points and then find the equation of the line through A and B.
2 - Example 1: Move points A and B so that they have the same y coordinates equal to -2. What is the equation of the line?
3 - Example 2: Move points A and B so that they have the same x coordinates equal to 5. What is the equation of the line?.
4 - Example 3: Move points A and B so that their coordinates are (1,2) and (0,5) respectively. Find an equation to the line through A and B in point slope form then rewrite in slope intercept form: y = m x + b.
5 - Example 4: Move points A and B so that their coordinates are (-3,0) and (5,4) respectively. Find an equation to the line through A and B in point slope form then rewrite in slope intercept form: y = m x + b.

## Solutions to the Above Examples

Solution to Example 1
It is a horizontal line (parallel to the x axis) and its equation is given by: y = - 2
Solution to Example 2
It is a vertical line (parallel to the y axis) and its equation is given by: x = 5
Solution to Example 3
First find the slope m = (5 - 2) / (0 - 1) = -3
The equation in point slope form can be written as y - 2 = -3(x - 1).
The equation of the line in slope intercept can be written as: y = -3 x + 5.
Solution to Example 4
First find the slope m = (4 - 0) / (5 - (-3)) = 1 / 2
The equation in point slope form can be written as y - 0 = (1 / 2)(x - (-3)).
The equation of the line in slope intercept can be written as: y = (1 / 2) x + 3/2.

## More References and Links on Lines and Slopes

Slope of a Line - Interactive Java Applet.
Easy to use calculator to find slope and equation of a line through two points.
Two Points Calculator
Easy to use alculator to find slope, x and y intercepts given the equation of a line.
Find Slope and Intercepts of a Line - Calculator