The standard form of an equation

A x + B y = C,

is most often seen in real-world examples of math problems. It describes the relationship between two variables when there is a restriction on how many things you can have in total.

Real-life problem

Suppose you are at the supermarket and want to buy one piece of fruit for your snack each day of the week. You need

7

pieces of fruit and you need to buy a combination of apples and oranges that gets you to

7 .

We can write this in an equation format:

Number of Apples + Number of Oranges = 7 .

With this we can have

6

apples and

1

orange, or

2

apples and

5

oranges, or any combination of the two fruits that adds to be a total of

7 .

The graph of this type of equation, because it shows a restriction and a combination of variables, is always a variation of the following format.

The $x -$ and $y -$ intercepts show the possible combinations where you have all of one kind of object and none of the other. In the example from before, the $x -$ and $y -$ intercepts would be the case when you had either $7$ oranges and $0$ apples or $7$ apples and $0$ oranges.

Exercise