What are the dependent and independent variables for the function y equals 6x plus 8?

The truth is that you can't actually answer, given the information you have. But that's not the answer you are looking for!

So, the equation you have is y = 6x+8.

There are two variables here, x and y. If you know what x is, you can calculate y as follows: you multiply x by 6 then add 8. So if x is 2, then 6 lots of x is 12, and adding 8 we get 20. So y is 20.

The general expression y = mx + c describes a linear relationship between two variables - m is referred to as the gradient and c is called the intercept. This is because if each of the pairs of x and y (e.g. x=2 and y=20 above), the line which join them intercepts (crosses) the y axis at 'c' and has a gradient (steepness) of 'm' (i.e. as you move one unit along the x axis, you go 'm' units up the y axis).

So which is dependent and which is independent? Earlier, we calculated y from x. This is the easiest thing to do with this equation. We can say that 'y is dependent on x' or 'x is the independent variable'. Mathematically speaking, though, we could just rearrange the equation (you can see that x = (y-8)/6 by taking 8 away from both sides and dividing both sides by 6). Then it looks like we've switched which one is dependent and independent. But we haven't really - and that is because you are not really asking a maths question, to do with equations, but a science question, to do with causes and effects.

In science, we often choose what x's we will use and measure the y's. *This* makes y dependent, but only if we choose it properly - it should actually change as a result of changing the x.

So y could be 'reading age' and x could be 'actual age in years'. Most people's reading age increases as they get older (at least up to a certain age). But it is how old they are that is causing their reading age to increase. So we would say that 'actual age in years' is the independent variable and 'reading age' is the dependent variable (because it depends on their actual age).

And so if we were doing an investigation into this relationship, it would be conventional to call the 'actual age in years' x and the 'reading age' y.

It is normal to call the independent variable 'x' and the dependent variable 'y'. I think that's what you really want to know, but it is important to know why.