1. Lesson 2.2 Linear Relations and Functions
By Nate Derrick
Period 6

2. Vocabulary Overview
Linear Relation: Relations that have straight line graphs
Nonlinear Relation: Relations that are not linear
Linear Equation: An equation that has no operations other than addition, subtraction, multiplication, of a variable by a constant
Linear Function: is a function written with ordered pairs that satisfy a linear equation
Standard Form: A form used to write linear equations (Ax+By=C)
y-intercept: y-coordinate of the point which the graph crosses the y-axis
x-intercept: x-coordinate of the point which the graph crosses the x-axis
These are all vocabulary terms used in the lesson

3. Major Topics Identifying a Linear Functions and Equations
Evaluate a Linear equation
Putting equations in standard form
Using intercepts to graph a line

4. Identifying Linear Equations and Functions
Has no operations other than addition, subtraction, multiplication, and division of a variable by a constant
Any function that can be written in y=mx+b or f(x)=mx+b is linear
No variable in denominator when Dividing, and No exponents greater than 1
Linear Equations and Functions: Non Linear Equations and Functions:
6y-x= x= 18/y
f(x) = 2 - x/ f(x)= 4-x³

5. Practice Problems Are the following equations and functions linear?
1.6x -2.4y = yx - 3y + 2x = 0
Yes No, variables can’t be multiplied by each other in a linear equation
f(x)= 4/x x - 4y= 16
No, because there is a variable in the denominator Yes

6. Evaluating a linear Equation
The Growth rate of a sample of bermuda grass is given by the function f(x) = 5.9x where f(x) is the total height in inches after x days after an initial measurement
How tall is the sample after 3 days
f(x) = 5.9x Original Function
f(3) = 5.9(3) Substitute 3 for x
20.95 inches Height of the sample after 3 days

7. Practice Problems
You want to make sure you have enough music for a car trip. If each CD is an average of 45 minutes long, the linear function m(x)= 0.75x could be used to find out how many CDs you need to bring.
How many hours of music are there on 4 CD’s
m(x) = 0.75x Original function
m(4) = 0.75(4) Substitute 4 for x
If you have 4 CD’s you have 3 hours of music

8. Using Standard form Always written in Ax + By = C
A, B, C are integers (positive or negative whole numbers)
No fractions or decimals in standard form
However the "Ax" term is positive
Write the following equations in standard form Identify A, B, and C
y = -4x - 7 Original Equation x = -2y - 1 Original Equation
4x + y= -7 Add 4x to both sides x + 2y = Add 2y to both sides
A = 4, b = 1, C = A = 3, B = 2, C = -1

9. Practice Problems Write the Equation in Standard Form
y = 6x Original Equation
-6x + y = Subtract 6x
6x - y = Multiply the Equation by -1

10. Practice Problems Write the Equation in Standard Form
-0.08x = 1.24y Original Equation
y = Subtract 1.24y
-8x - 124y = Multiply the Equation by 100
8x + 124y = Multiply the Equation by -1

11. Using Intercepts to Graph a line
Find the x-intercept and the y-intercept of the graph 2x - 3y + 8 = 0
Plug in the coordinate (0,0) then solve
2x - 3(0) + 8 = 0 2(0) - 3y + 8 = 0
2x = y= -8
x= y= 8/3

12. Practice Problem
Find the x and y intercepts of the graph 2x + 5y - 10 = 0
2x + 5(0) - 10 = (0)+ 5y - 10 = 0
2x - 10 = y - 10 = 0
2x = y = 10
x= y = 2

13. Practice Problem
Graph