Finding the equation of a straight line

Finding the equation of a straight line from two points

Let’s suppose we know that two points are on a straight line - and - and we want to find the equation of that straight line.

We need to know the gradient if we want to find the equation of the line, and after that, we can substitute in our values for , , , and into the equation of a straight line: .

Finding the gradient

The gradient of a graph can be found by calculating the change in divided by the change in , or:

• The change in is going to be the difference between the starting value - - and the ending value - , so .
• The change in is going to be the difference between the starting value - - and the ending value - , so .

So, the gradient can be calculated using:

Finding the equation of the line

Once you have found the gradient, you can substitute it into the equation of a straight line:

Example: find the equation of the straight line that passes through the points (2, 3) and (5, 11)

• Find the gradient:
• Substitute into the equation of a straight line:
• We can rearrange this into the form if we want to:
• Answer:

Example: find the equation of the straight line that passes through the points (1, 4) and (3, 10)

• Find the gradient:
• Substitute into the equation of a straight line:
• We can rearrange this into the form if we want to:
• Answer: