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Linear Equations

So maybe you've seen the familiar equation y = mx + b, or something like y = 4x - 7. Why is this important? What can we do with this? Why do we have to have all these x's and y's?

Well, let's think about a real life example. Let's say we go into the grocery store to buy some cereal and that's it. We want to determine how much it is going to cost us to buy a certain number of boxes of cereal. For example purposes, let's assume each box of cereal we buy costs $2.00. We can write an equation that shows the relationship between our total cost and the number of boxes of cereal we buy. We can write:

Total cost = (total number of boxes of cereal) times ($2.00 per box of cereal)

Makes sense right? If we buy 1 box of cereal, our total cost is $2.00 before taxes. If we buy 2 boxes, our total cost is $4.00, etc. etc. Well, why don't we let y = total cost and let x = the total number of boxes of cereal we buy. Can't we rewrite our about equation like this:

y (total cost) = x (total number of boxes of cereal) times ($2.00 per box of cereal) OR

y = 2x

where:
y = total cost
x = total number of boxes of cereal purchased

We just took a real life example and turned it into an algebraic, linear equation that shows the relationship between two unknown quantities (or variables). Now that we have an equation, we can pick and chose any number for x (which is our input), and we can determine what y is (which is our output). If we buy 3 boxes of cereal, we plug in 3 for x, and we get 6 for y, so our total cost would be $6.00.

So when you see x's and y's in algebraic equations, remember all we are doing is simply modeling mathematically the relationship between two variables. Think about how you apply this to everyday life. You can do it!

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