Course: 8th Grade Math
DETAIL LESSON PLAN
Student Objective
8.F.A.3-1 Interpret the equation y=mx + b as defining a linear function, whose graph is a straight line
8.F.A.3-2 Give examples of functions that are not linear, meaning that the points when graphed do not form a straight line.
Lesson
Identifying Linear and Non-Linear Functions
Homework
Teacher selected
Bellwork
Teacher selected
Prior Knowledge
 Review bellwork
 Review homework
Introduction

TODAY, we will learn how to identify and graph linear and non-linear equations.
Teacher Input
 Pass out student notes.
 Talk a little bit about the real world example of “linear”.
 Review student notes on linear equations.
 Talk a little bit about the real world example of “non-linear”.
 Review student notes on non-linear equations.
 Classwork: Linear and Non-linear Worksheet
Assessment
Question the students for understanding. Observe students as they work on classwork/homework.
Closure
Teacher selected
Linear equations are equations that make a straight line when graphed!
Nonlinear equations are equations that DO NOT make a straight line when graphed.
U-Shape
V-Shape
S-Shape
For the adventurous “Zip Lining” can be a great way to do a
little sightseeing. The steepness of the zip line is the
slope. Slope is an example of a relationship that is linear!
Hawaii
Linear equations are equations that make a straight line when graphed.
Slope-Intercept Format
Any equation in what we call “Slope-Intercept” form will always
graph to be a straight-line.
Slope-Intercept Form
slope
y-intercept
slope
y-intercept
Examples – Below are two equations in slope intercept form. Complete the
function tables below, and then graph. What shape do the graphs make?
1)
2)
Linear Equations can be presented in forms other than y = mx + b.
Examples: Complete the function table, and then graph.
What shape do the graphs make?
1)
Question:
Could this equation be changed
so that it is written in slope-intercept form?
2)
Question:
How about this equation, could it
be changed so that it is in slope-intercept form?
When you kick a ball in the air, the path that the ball
follows is a curve called a parabola.
A parabola is an example of a relationship that is not linear.
Nonlinear equations are equations that DO NOT make a
straight line when graphed.
Today, we will discuss three types of non-linear equations that graph to form
the shape of a “U”, “V”, or “S”.
Graphing Non-Linear Equations
Let’s take a look…
Complete each table, and then graph. What shape does the graph make?
1)
Shape_____
2)
Shape_____
3)
Shape_____
Characteristics of Non-Linear Shapes
U-shaped
If the x is squared, x², the equation when graphed will form a U-shaped curve
called a parabola.
 Rhyme:
The power of 2 will make a U.
 y = x² + 5
If the x is positive the U will open up.
 y = -x² + 2
If the x is negative the U will open downward.
V-shaped
If the x is an absolute value, |x|, the equation when graphed will form a
V-shaped figure.
 Trick:
The symbol | | snaps to form a V.
 y = |x| + 5 If there is a positive outside the ||
the V will open up.
 y = -|x| + 2 If there is a negative outside the ||
the V will open downward.
S-shaped
If the x is cubed, x³, the equation when graphed will form an S-shaped figure.
 These equations will form an S-shape.
 Example graphs of an S-shape.
y = x³ + 2,
2 x³+1
Name: _______________________
Period: _________
Linear & Non-Linear
Equations
Classwork
Directions: Without graphing, predict the shape of the following equations.
(straight line, u-shaped, v-shaped, or s-shaped)
1.
y = |x| + 1
__________________
11.
y
6
__________________
2.
y = 3x + 4
__________________
12.
6x + 3y = 12
__________________
3.
y
x
__________________
13.
y
__________________
4.
y
3
__________________
14.
4x + y = 1
__________________
5.
y = x³
__________________
15.
y
12x + 7
__________________
6.
y
__________________
16.
y
x³ + 4
__________________
7.
y
__________________
17.
y
x
__________________
8.
y
__________________
18.
y
2x
__________________
9.
y= x
2
__________________
19.
y = 3 + x²
__________________
10.
y
2x³ +1
__________________
20.
y=
__________________
21.
Describe each equation as linear or non-linear.
8
x
x
2x
3
2
5x
3
a. y = 8 × 5x
__________________
b. y = (3x + 10)²
__________________
c. y = 11x²
__________________
d. y = 12x – 3
__________________
e. y = 3x³ + 2
__________________
x
2x
4
6
x² + 1
Directions: For each function, complete the table for integer values of x from -2 to 2.
Then graph each function and name the shape.
Name Shape
1)
2)
3)
4)
Answer Key
Linear equations are equations that make a straight line when graphed.
Slope-Intercept Format
Any equation in what we call “Slope-Intercept” form will always
graph to be a straight-line.
Slope-Intercept Form
slope
y-intercept
slope
y-intercept
Examples – Below are two equations in slope intercept form. Complete the
function tables below, and then graph. What shape do the graphs make?
1)
2)
Linear Equations can be presented in forms other than y = mx + b.
Examples: Complete the function table, and then graph.
What shape do the graphs make?
1)
Question:
Could this equation be changed
so that it is written in slope-intercept form?
Yes
. So, the point is that any equation that can be
rewritten in slope- intercept form will graph to be a
straight line.
2)
Question:
How about this equation, could it
be changed so that it is in slope-intercept form?
Yes
Here again, any equation that can be rewritten in
slope- intercept form will graph to be a straight Line.
Nonlinear equations are equations that DO NOT make a
straight line when graphed.
Today, we will discuss three types of non-linear equations that graph to form
the shape of a “U”, “V”, or “S”.
Graphing Non-Linear Equations
Let’s take a look…
Complete each table, and then graph. What shape does the graph make?
1)
Shape
2)
Shape
3)
Shape_____
Characteristics of Non-Linear Shapes
U-shaped
If the x is squared, x², the equation when graphed will form a U-shaped curve
called a parabola.
 Rhyme:
The power of 2 will make a U.
 y = x² + 5
If the x is positive the U will open up.
 y = -x² + 2
If the x is negative the U will open downward.
V-shaped
If the x is an absolute value, |x|, the equation when graphed will form a
V-shaped figure.
 Trick:
The symbol | | snaps to form a V.
 y = |x| + 5 If there is a positive outside the ||
the V will open up.
 y = -|x| + 2 If there is a negative outside the ||
the V will open downward.
S-shaped
If the x is cubed, x³, the equation when graphed will form an S-shaped figure.
 These equations will form an S-shape.
 Example graphs of an S-shape.
y = x³ + 2,
2 x³+1