Function Notation and Linear Functions
Key Questions

First, convert the linear equation to slopeintercept form. The slopeintercept form of a linear equation is:
#y = color(red)(m)x + color(blue)(b)# Where
#color(red)(m)# is the slope and#color(blue)(b)# is the yintercept value.Then switch out the
#y# variable for#f(x)# :#f(x) = mx + b# 
Answer:
A function is a set of ordered pairs (points) formed from a defining equation, where, for each
#x# value there is only one#y# value.Explanation:
#x> y# represents a functionThis means that you can choose an
#x# value and plug it into an equation, usually given as:#y= ....." " or" " f(x)= .....# This will give you a
#y# value.In a function there will be only ONE possible answer for
#y# .If you find you have a choice, then the equation does not represent a function.
The following are functions:
#y=3# #y=3x5# #y = 2x^23x+1# #(1,2), (2,2), (3,2),(4,2)# The following are NOT functions:
#x= 3# #y=+sqrt(x+20)# 
We can do more than giving an example of a linear equation: we can give the expression of every possible linear function.
A function is said to be linear if the dipendent and the indipendent variable grow with constant ratio. So, if you take two numbers
#x_1# and#x_2# , you have that the fraction#{f(x_1)f(x_2)}/{x_1x_2}# is constant for every choice of#x_1# and#x_2# . This means that the slope of the function is constant, and thus the graph is a line.The equation of a line, in function notation, is given by
#y=ax+b# , for some#a# and#b \in \mathbb{R}# .
Questions
Graphs of Linear Equations and Functions

Graphs in the Coordinate Plane

Graphs of Linear Equations

Horizontal and Vertical Line Graphs

Applications of Linear Graphs

Intercepts by Substitution

Intercepts and the CoverUp Method

Slope

Rates of Change

SlopeIntercept Form

Graphs Using SlopeIntercept Form

Direct Variation

Applications Using Direct Variation

Function Notation and Linear Functions

Graphs of Linear Functions

Problem Solving with Linear Graphs