Here's a different perspective. This is an excellent question because it gets right to the heart of something that often causes confusion. How do we deal with an equation that seems to have five variables? The answer is that it really has only two variables. Three of the symbols that look like variables are actually placeholders for constants. We’re using symbols to represent those constants as a way of generalizing a solution. In other words, we want a formula that solves a whole class of problems rather than just one problem.
In this case, we’re trying to solve a problem in which we’re given three numbers -- the slope of a line, the x-coordinate of a point on that line, and the y-coordinate of that point -- and our task is to find an equation for that line. For example, we might be told the slope is 2, and the line goes through a point with x-coordinate 3 and y-coordinate 5. After a little work we can come up with an equation that satisfies those conditions. Then we get another three numbers: slope = -3, x-coordinate = 2, y-coordinate = 17. Again we work with these three numbers and come up with an answer.
After solving problems of this kind many times we see that it would be easier to have a template we can use to plug in these three numbers and get a solution right away. In this template we need placeholders for the three constants we’re going to be working with. We could produce a perfectly valid template in which they’re called a, b and c, but we can reduce the potential for confusion, and produce a more revealing template, if we give these placeholders names that correspond with how they’re used. We’ll use the traditional symbol for slope, which is m, and we’ll use x with a subscript to designate the constant we’re given for the x-coordinate of the point and y with a subscript for the y-coordinate. We could use any subscript here, but the choice of 0 is conventional. Using the same subscript for x and y tells us that these constants are related: they’re coordinates of the same point. And here’s what we get:\[y-y_0=m(x-x_0)\]So now, any time we’re given the slope of a line and the coordinates of a point on the line, all we have to do to produce an equation for that line is plug those constants into this template where the corresponding placeholders appear. No more thinking required!
In calculus you’ll be dealing with many equations that use placeholders for constants. There’s no hard and fast rule that tells you which of the letters in an equation are variables and which represent constants. Sometimes this will be stated as part of the problem, but other times you have to determine this from the context of the problem. A subscript often indicates a constant, but in the equation above we also have m without a subscript as a constant. We know m is a constant because this is the point-slope formula for the equation of a line, the one we use to find the equation when we’re given the slope and the coordinates of one of the points on the line.