Linear Functions are functions that have a constant rate of change. The graph of a linear function is a line, whose slope can be found algebraically and graphically as the constant rate of change.
The slope of a line is the ratio of the vertical change to the horizontal change between two points the line passes through. The variable is commonly used to represent the slope.
This chapter shows a few different ways to graph linear functions, such as using a table of values, using the and intercepts, and using the slope and intercept.
The function rule of a linear function can be written in different ways. The most commonly used is the Slope-Intercept Form, where indicates the slope and indicates the intercept. Another way to write the function rule of a linear function is the Standard Form.
Linear functions that have a positive slope are increasing and if they have a negative slope they are decreasing. If a linear function has a slope of it is parallel with the axis and commonly referred to as a constant function.
In this chapter we will also explore the effects of transformations on linear functions in both the rules and the graphs of the functions. Linear inequalities are also introduced and graphed, demonstrating their solution sets as half-plane regions of coordinate planes.