# Linear Functions

## What does it mean?

### Definitions:

A function is a mathematical relation such that each element of a given set (which is called the domain of the function) is associated with an element of another set (the range of the function).

It is often written as "f(x)" where x is the input value.

A linear function is a function that can be graphically represented in the Cartesian coordinate plane as a straight line.

## What does it look like?

A general example to help you recognize patterns and spot the information you're looking for

Write down the equation of the line that passes through the two points $$(-2, 4)(3, -5)$$ We can use these two points to determine the missing slope of the line. $$m = \frac{x_2 - x_1}{y_2 - y_1}$$ $$m = \frac{3 - (-2)}{(-5) - 4}$$ $$m = -\frac{5}{9}$$ Now, use any of the given points to write down the equation of the line. We’ll use (-2, 4) $$y = 4 - \frac{9}{5}(x + 2)$$ $$y = \frac{20}{5} - \frac{9}{5}x + \frac{18}{5}$$ $$y = -\frac{9}{5} + \frac{2}{5}$$

## You'll use it...

We use them when we want to estimate if sales will grow or decline.

## Video

### Function Example Problems

Watch a Khan Academy Video »
Length: 11:49

## Video

### X and Y Intercepts

Watch a Khan Academy Video »
Length: 3:25