The standard way to arrange a straight line graph equation is y = mx + c is
So if you are given an equation like this 4y – 8x = 5 then you should rearrange it into the standard form:
4y – 8x = 4
So 4y = 8x + 4
So y = 2x + 1
Once in this format you know the following things:
- m is the value of the gradient (so in this example the gradient is 2)
- c is the value where the line crosses the y axis – so here the graph has the point (0,1)
This is handy because if you have to plot it you already have one point on the graph!
You might also be asked to find the equation for a given line in the format y = mx + c. So let’s take an example to show how you do it. Look at the following graph:
We can see the graph goes through the y axis at (0,3) therefore we know that the value of c is 3.
We now need to find the gradient. Let’s take the points (0,3) and (3,-3).
Change in y = 3 –3 = 3+3 = 6 (remember – minus a minus is a plus!)
Change in x = 0 – 3 = -3 (remember minus a minus is a plus!)
Therefore the gradient is 6/-3. So the gradient is -2.
We therefore have a value for m and c so we can write the graph in standard form.
y = -2x + 3