GCSE Maths What on Earth is y mx c 2026 27 exams

in this video we're going to look at why the equations for lines on graphs all tend to look like this rather than any of the other ways that we could have written them essentially it's just for convenience by always writing the equations in the form of equals plus they're all in the same format which makes it easier to quickly compare them and imagine what they'd look like when drawn out on graph the important things to know about this form are that is the gradient of the line which remember is measure of how steep the line is and is the y-intercept which is the point where the line crosses the y-axis for example if we took this equation equals 2x plus 3 then would be 2 because that's the number in front of the and would be positive 3. this means that if we had graph and we wanted to sketch this line we know that it would cross the y-axis here because the y-intercept is 3 so we'll cross the y-axis at equals 3. then because our gradient is two we know that for every one place that our line moves across it'll move up by two places so it will also go through this point here and then all we have to do is draw line between these two points and extend it across the whole graph and that will be our line however if we had been given our equation in this other form two minus four equals six then we couldn't have used this technique to sketch it instead we'd have had to rearrange it into the form of equals mx plus first to do this which just add 4x to both sides to get 2y equals 4x plus 6 and then divide both sides by 2 to get equals 2x plus 3. and now that it's in the form of equals mx plus we know both the gradient and the y-intercept so we can plot it let's try doing the same thing for this equation 4y plus 16 equals 2x the first thing we need to do is rearrange it to get it into the form of equals mx plus so we need to subtract 16 from both sides to get 4y equals 2x minus 16 and then divide both sides by 4 so that we only have single on the left which will equal one half minus four on the right then if you compare this to equals plus you can see that will be minus four so the line will intercept the axis just here at -4 and also that is one-half so the gradient of the line will be one-half this means that for every one that the line goes across on the x-axis it's going to go up by one half so by plotting couple of points like this we can see that the line's going to go through all of these points and so look like this now the last thing want to mention is that you'll sometimes see equations like these which might look like they're not in the form of equals mx plus because this one doesn't have value and this one doesn't have an however if there's no number after the term you can just think of it as plus zero so is zero which means that it crosses the axis at equals zero and the 3x tells us that the line has gradient of 3. for the other one if there's no number in front of the then it's effectively 1x so the gradient is one and the plus four tells us that it intercepts the y-axis at positive four anyway that's everything for this video so hope that all made sense and thanks for watching