# Find Equation of a Line

## Equation of line in Point Slope FormThe 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:_{B} - Y_{A}) / (X_{B} - X_{A})
then the equation of the line in point slope form given by
_{A} = m (x - x_{A})
_{B} = m (x - x_{B})
## Interactive Tutorial with Examples and Solutions1 - 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 ExamplesSolution to Example 1It is a horizontal line (parallel to the x axis) and its equation is given by: y = - 2 Solution to Example 2It is a vertical line (parallel to the y axis) and its equation is given by: x = 5 Solution to Example 3First 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 4First 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 SlopesSlope 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 |