1. Linear and Non-Linear Functions
y = 2x + 1
y = 𝟔 𝒙
8th Grade Math
Presented by Mr. Laws

2. CCSS Standard
8.F.3 - Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear.
8.F.4 – Find slope: Construct a function to model a linear relationship between two quantities.

3. Essential Question
How do I define a linear function, and how do I identify examples of functions that are not linear?

4. What is a Linear or Non-Linear Function?
A linear function is a specific function when graphed, will form a straight line on a coordinate plane.
A non-linear function is a specific function when graphed, will not form a straight line on a coordinate plane.
A linear function can be represented by a graph, a equation, or a function table.

5. Linear Function (Graph)
A linear function graph is a set of order pairs (x,y) when plotted will form a straight line on a coordinate plane. y x y x y x y x
Since these graphs displays a straight line, these are linear graphs.

6. Non-Linear Function (Graph)
A non – linear function graph do not display a straight line. y x y x y x y x
Non-Linear Graphs

7. A Linear Equations y = mx + b y = 1 2 x – 6 y = 2x + 1 y = 3x y = 1
A linear equation is an equation when graphed on a coordinate plane, will form a straight line.
It is based on a math formula called slope intercept form (SIF):
slope
y = mx + b
input
output
y- intercept
Examples:
y = x – 6
y = 2x + 1
y = 3x
y = 1
y = 𝑥 6
y = -x – 1
y = x – 5
y = -x
y = -7

8. Non-Linear Equations Examples: y = 𝟔 𝒙 y = 2x2 + 1 y = 8x2 + 1x y = 4x
Non – Linear equations are equations when graphed, will not form a straight line.
Non – Linear equations do not match slope intercept form (y=mx+b).
Examples:
y = 𝟔 𝒙
y = 2x2 + 1
y = 8x2 + 1x
y = 4x

9. Linear Function Table X Y
Linear Function tables are functions tables when graphed on a coordinate plane, will form a straight line.
For it to be a linear function, both the x-value and y- value must have a constant rate of change.
+ 2
+ 1
The x-value has a constant rate of change of plus 1. X 1 2 3 4 5 Y 6 8 10
The y-value has a constant rate of change of plus 2.
Since both x and y value have a constant rate of change, this is an linear function table.
Constant rate of change = 𝐶ℎ𝑎𝑛𝑔𝑒𝑠 𝑜𝑓 𝑦 𝐶ℎ𝑎𝑛𝑔𝑒𝑠 𝑜𝑓 𝑥

10. Non-Linear Function Tables
Non - Linear Function tables are functions tables that do not have a constant rate change in either the x-value or y-value or both.
+ 1
+ 1
+ 1
+ 1
The x-value has a constant rate of change of plus 1. X 1 2 3 4 5 Y 8 12 20
The y-value does not have a constant rate of change. This function table is non-linear.
+ 1
+ 5 +4
+ 8

11. Summary Can you answer the essential question?
Do you have any questions on what you have learned?
Will you be able to write a summary based on the lesson?