Here's a video that shows graphs in action.
When you have an equation like 2x + 3y = 6 and no other clues, sometimes all you can do is plug in numbers randomly and hope that everything works out.
No, seriously. That's a real math thing.
Take that equation, for example. If you plug in a few random numbers for x, you might notice that you get results like these:
x = 0, y = 2
To represent this data visually, we draw a graph with an x-axis and a y-axis and plot these points like so:
Either those dots are starting to form a line, or that’s an awfully big coincidence. (It’s the first one.) If you keep plugging in random numbers, you'll continue to get points that fall along this same line. It's mathmagic. You can therefore represent all the possible solutions for both variables by connecting the dots on your graph.
As with all algebra, we're not just talking about some arbitrary line and some arbitrary grid. This line can be used to represent real information. Think about that vegetable garden you were tending. (Can't remember? Oh, that's right, we were the ones counting your vegetables.) If your tomatoes seem to be growing at the same rate as your onions, you should be able to predict how many onions grow in your garden for every tomato. This data is important, because you have to know how many toppings you’ll be able to put on top of your burger.