Question

What does it mean for an equation to express y in terms of x

Answer 1

An equation expresses the relation between variables. A relation between y and x can be drawn as a graph in the xy plane.

In order to do that, you want to "plug in" a value for x, and then get the result as a value for y. With an equation that expresses y in terms of x, you can do just that. For example, plug in the value x=3 in the equation y=2x+4 easily gives you y=10. You plot the point (3,10) and repeat for different x.

If y is not clearly expressed in terms of x, you get equations like: 2x + 4y + x/y = 0. You cannot plug in an x and calculate a y in an easy way.

Most of the time you'll be able to rewrite the equation in the right "pluggable" form. In fact, when you have an equation in this form, it maps one to one to a function f(x). y=2x+4 and f(x)=2x+4 is kind of the same thing. "f is a function of x" and "y is expressed in terms of x" are similar statements.