SOLUTION: What is the difference in a linear equation and a linear function? What 'real world' businesses use linear equations/functions?

Question 4339: What is the difference in a linear equation and a linear function? What 'real world' businesses use linear equations/functions?
Answer by rapaljer(4671) (Show Source): You can put this solution on YOUR website!
A linear expression is an expression involving a variable whose highest power is 1. Examples of linear expressions would be 2x+4, 5x-25, x+5, 5x-12, etc.

A linear equation is an equation involving a variable whose highest power is 1. Examples of linear equations would be 2x+4=0, 5x-25=0, x+5=3x-2, 5x-12=3x, etc.

A linear function involves a second variable, like y, and a variable like x whose highest power is 1. Examples of linear functions would be y=2x+4, y=5x-25, y=-3x+12, etc.

Notice that there is NO equal sign in an expression, so you can't solve it. In fact there is not much you can do with an expression. You can factor it (sometimes but not always!), but that's about it.

With an equation, you must have an equal sign, a left side, and a right side. Because of the equal sign, you can solve the equation. The solution is always in the form of x= some number, which can be graphed on a numberline.

With a function, there is a second variable (usually y) involved, which means that the function can be graphed in two dimensions on what we call a Cartesian coordinate system (named after Rene Descartes, who is credited with coming up with the idea of graphing two variables in two dimensions).

Almost any real world business can at some level make use of linear equations/functions. For example, graphing linear functions is absolutely required for any statistics course. If your major requires statistics, you will see that graphing lines are essential in order to compare one variable to another. Slopes of lines are essential, not only in statistics, but highway construction, railroads, construction (landscape and roofing slopes!). In every business, you will need to compare existing data of company sales, revenue, profit, etc. in order to project future sales, revenue, profit, etc. Business decisions in all areas of life are made using statistics, and linear functions (graphs of lines!) are an important part of those decisions.

Perhaps some of our other tutors will elaborate further based upon their experiences in other fields of business and life in other parts of the world.

R^2 at SCC

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