The linear function is popular in subjects such as economics and physics. It is attractive because it is simple and easy to handle mathematically. Besides its uses in physics and economics, linear functions have many important applications.

These real-life problems are converted into mathematical forms to form linear equations which are then solved using various methods. It should clearly explain the relationship between the data and the unknowns (variables) in the situation. Below mentioned are examples of real-world applications of linear functions:

• Age problems

• Speed, time, and distance problems

• Geometry problems

• Money and percentage problems

• Wages and hourly rate problems

• Force and pressure problems

• relation: A collection of ordered pairs.

• variable: A symbol that represents a quantity in a mathematical expression, as used in many sciences.

• linear function: An algebraic equation in which each term is either a constant or the product of a constant and (the first power of) a single variable.

• function: A relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output.

Linear functions are algebraic equations whose graphs...

• have a constant slope,

• are straight lines

• cut the y-axis at a single point.

Summarizing:

It was shown above that the slope of a linear function between any two points is a constant regardless of the two points chosen. So to find the slope of a line, we only need any two points.

We have also learned that given two points on a line, its slope is described as the rise (difference in the y-coordinates) over to divide by the run (or difference in x-coordinates).

Before, you will see the slope formulae is used to get the slope-intercept function. The two points chosen are (0, b) and (x, y).

NOTE: the point (0,b), is a point on the y-axis