How do I find out the equation of a line?

First of all, we must remember the formula for the equation of a line.

This is y=mx+c.

It is important to understand what each part of the equation means:

-y is the y-coordinate of any point on the line
-x is the x coordinate of the point on the line
-'m' stands for the gradient of the line
-'c' indicates the y-intercept (the point at which the line crosses the y axis)

1. Pick a point on the line to get your x and y co-ordinates. We want to try and use whole numbers where possible to make our sums easier.

2. Next, we can find the gradient of the line by finding the change in x/change in y (or some may know this as step/rise).
To do this, we need to find another point on the line, therefore to find the change we will do x₁-x₂/y₁-y₂.

Be careful here to note whether the line is a positive or negative gradient, as it is easy to get confused. If your answer is outside the ranges of -1 to 1, something in your math is wrong.

3. Once you have found your gradient the only other unknown is c. Substitute your value of m and the coordinates of any point on the line into your equation and rearrange to find the value of c.

The easiest way to do this is usually to subtract mx from both sides leaving us with y-mx=c.

4. To finish, write your equation of the line with your values of m and c, but do not put values into x and y are these are not constant values.