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.
'W' and 'L' are independent variables. 'P' is the dependent variable. '2' and '2' are the constants.
You cannot solve 1 linear equation in 2 unknown variables. You need at least two independent equations.
Is an equation of a straight line in 3 dimensions. It cannot be simplified further, and a solution for any of the variables requires another two [independent] equations.
2
determine whether each relation is a function y equals -8
As it is written, x is the independent variable and y is the dependent. But you could re-write it as x = y/23 + 30/23 and then y is the independent variable and x the dependent.
'W' and 'L' are independent variables. 'P' is the dependent variable. '2' and '2' are the constants.
Both. If you look at it like this: y=41-x you say x is independent and y is dependent of x (i.e. y is a function of x) For x=41-y you say y is independent and x is dependent of y (i.e. x is a function of y)
2
Total Cost (T) = Fixed Cost (F) plus Variable Cost (V) or T = F + V. The dependent variable is T because as F & V change, T depends on the values of F & V. The independent variables (plural; two) are F & V. F and V change independent of T. You can also think of the above as cause (independent) and effect (dependent). The cause of F & V changing has the effect of T changing. So, in the above equation, there are two independent variables; F & V.
You need two independent linear equations to solve for two unknown variables.
You need three independent equations to solve for three unknown variables.
3
Yes. It has variables x, y etc and their powers.
It is an equation in two variables, c and g.
To solve for two unknown variables (x and y) you require two independent equations,
To solve for 2 unknown variables you need 2 independent equations. You have only 1.