We often see math applied to the real world through word problems, and the applications of linear equations are seen throughout all our math courses after Algebra. To understand applications of linear equations we need to have an understanding of slope, how to interpret a graph, and how to write an equation. In upper-level Algebra, we apply systems of linear equations to these problems as well.
I'm a math teacher. And one of the things students ask me all the time is when are we going to use this in the real world? And a lot of the times, you guys, you really do use math in the real world. And one of the situations you're going to see those kind of situations in your math class is using graphs that describe linear equations or word problems.
When you're looking at a word problem or a graph that describes a word problem, there's a bunch of things to keep in mind. One thing to be really sure you're aware of is the scale on the X and the Y axis. By scale, that means how much are you counting by? Are you counting by 5s or counting by 500s. That's something that's really important in terms of the real world context.
Along those same lines, pay attention to the units. Units meaning are you looking at how much you're paying in dollars or pounds or yen or cents or whatever it is. All those kinds of units are really important to keep in mind especially when you get to the slope.
One of the most common graphs of word problems is about slopes of distances and times, because the slope is distance per time. It's the rate. It's how fast you're traveling. So a lot of times you're going to be asked to interpret the slope of a word problem graph.
Another thing I want you guys to keep in mind is the intercepts and what the intercepts mean on a graph. Keep in mind that the X intercept means the Y quantity is equal to 0 .Y intercept means X quantity is equal to 0.
When you're looking at graphs all of these things are really important to keep in mind and it will help you connect this math to the real world.