Unit 3
Linear Functions and Patterns
Big Idea: Linear Functions and Patterns
Objective: The student will learn how to
interpret graphs
Common Core Mathematics Standard 2
2
Interpret graphs
Read GET READY for the Lesson, p. 53
What does the point B on the graph represent?
About what percent of normal blood flow occurs
two days after the injury?
On what does the percent of blood flow depend?
Vocabulary
function
Interpret graphs
A relation between input
and output.
In a function, the output
depends on the input.
Vocabulary
Coordinate system
Interpret graphs
Used to graph a function
Formed by the
intersection of two
number lines, the
horizontal axis and
vertical axis
Vocabulary
Coordinate system
Interpret graphs
Used to graph a function
Formed by the
intersection of two
number lines, the
horizontal axis and
vertical axis
Interpret graphs
Vocabulary
Vertical axis : y-axis
Origin : (0, 0)
(3, 2)
Ordered pair
(x, y)
Horizontal axis :
x-axis
I / WE / YOU DO
I / WE DO
- Example 1, p. 53
YOU DO
-√ Your Progress, p. 53 #1
Interpret graphs
Vocabulary
Interpret graphs
In the example the blood
flow depends on the
number of days since the
injury.
Independent variable
The number of days since
the injury
Dependent variable
The percent of normal
blood flow
I / WE / YOU DO
I DO
- Example 2, p. 54
WE DO
- √ Your Progress - p.54 #2A
YOU DO
- √ Your Progress - p.54 #2B
Interpret graphs
I / WE / YOU DO
I / WE DO
-Example 3, p. 54
YOU DO
-√ Your Progress - p.54 #3
Interpret graphs
I / WE / YOU DO
I / WE DO
-Example 4, p. 55
YOU DO
-√ Your Progress - p.55 #4
Interpret graphs
Practice
Interpret graphs
Demonstration of learning – p. 56 # 1 - 7
p. 56-58 # 10 - 21
Big Idea: Linear Functions and Patterns
Objective: The student will learn how to
graph linear equations using x and y
intercepts
Common Core Mathematics Standard 2
14
Graph using intercepts
Read GET READY for the Lesson, p. 155
If a person consumes an average of 2000
calories per day, how many grams of fat
should the person consume?
How can you use the graph to answer the
question?
Vocabulary
Linear equation
Standard form of a
linear equation
Graph using intercepts
The equation of a
straight line
𝑨𝒙 + 𝑩𝒚 = 𝑪
I / WE / YOU DO
I DO
- Example 1, p. 155
WE DO
-√ Your Progress - p. 156 #1A
YOU DO
-√ Your Progress - p. 156 #1B
Graph using intercepts
Vocabulary
Graph using intercepts
X-intercept
The x-coordinate of the
point where the graph of
an equation crosses the
x-axis
y-intercept
The y-coordinate of the
point where the graph of
an equation crosses the
y-axis.
Vocabulary
Graph using intercepts
y-intercept : (0, y)
(0, 4)
x-intercept : (x, 0)
(3, 0)
I / WE / YOU DO
I DO
-Example 2, p. 156
WE DO
-√ Your Progress - p. 156 #2A
YOU DO
-√ Your Progress - p. 156 #2B
Graph using intercepts
I / WE / YOU DO
I / WE DO
-Example 3, p. 157
YOU DO
-√ Your Progress - p. 157
#3
Graph using intercepts
I / WE / YOU DO
I DO
-Example 4, p. 157
WE DO
-√ Your Progress - p. 157 #4A
YOU DO
-√ Your Progress - p. 157 #4B
Graph using intercepts
I / WE / YOU DO
I / WE DO
-Example 5, p. 158
YOU DO
-√ Your Progress - p. 158 #5
Graph using intercepts
Practice
Graph using intercepts
Demonstration of Learning – p. 158 # 1 - 11
p. 159-160
- Identify linear equations and write in standard form
#12 -17
- Determine intercepts of each function
#18 - 23
- Graph a linear equation using a table or intercepts
#24 – 32
- Applications
#33 – 38; 53 - 55
Big Idea: Linear Functions and Patterns
Objective: The student will learn how to
solve problems using slope of a line.
Common Core Mathematics Standard 2
25
Slope of a line
Read GET READY for the Lesson, p. 187
What is the slope of the roof if the rise is 10 and
the run is 6?
What might the rise and run be for a roof with
a slope of 2?
Vocabulary
Rate of change
rate of change =
Slope of a line
A ratio that describes, on
average, how much one
quantity changes with
respect to another
quantity
𝒄𝒉𝒂𝒏𝒈𝒆 𝒊𝒏 𝒚
𝒄𝒉𝒂𝒏𝒈𝒆 𝒊𝒏 𝒙
The table on p.187 shows the
distance a person has walked
for various amounts of time
Slope of a line
rate of change = 𝒄𝒉𝒂𝒏𝒈𝒆 𝒊𝒏 𝒚
𝒄𝒉𝒂𝒏𝒈𝒆 𝒊𝒏 𝒙
rate of change =
𝒄𝒉𝒂𝒏𝒈𝒆 𝒊𝒏 𝒅𝒊𝒔𝒕𝒂𝒏𝒄𝒆
𝒄𝒉𝒂𝒏𝒈𝒆 𝒊𝒏 𝒕𝒊𝒎𝒆
𝟒 𝒇𝒆𝒆𝒕
rate of change =
𝟏 𝒔𝒆𝒄𝒐𝒏𝒅
This means that the person
walked 4 feet per second
I / WE / YOU DO
I DO
-Example 1, p. 187
WE DO
-√ Your Progress - p. 188 #1A
YOU DO
-√ Your Progress - p. 188 #1B
Slope of a line
I / WE / YOU DO
I / WE DO
-Example 2, p. 188
YOU DO
-√ Your Progress - p. 188 #2
Slope of a line
Slope of a line
𝒓𝒊𝒔𝒆
slope =
𝒓𝒖𝒏
(4, 5)
(1, 3)
I / WE / YOU DO
I DO
- Example 3, p. 190
WE DO
-√ Your Progress - p. 190 #3A
YOU DO
-√ Your Progress - p. 190 #3B
Positive slope of a line
I / WE / YOU DO
I DO
- Example 4, p. 190
WE DO
-√ Your Progress - p. 190 #4A
YOU DO
-√ Your Progress - p. 190 #4B
Negative slope of a line
I / WE / YOU DO
I DO
- Example 5, p. 190
WE DO
-√ Your Progress - p. 190 #5A
YOU DO
-√ Your Progress - p. 190 #5B
Zero slope of a line
I / WE / YOU DO
I DO
- Example 6, p. 191
WE DO
-√ Your Progress - p. 191 #6A
YOU DO
-√ Your Progress - p. 191 #6B
Undefined slope of a line
I / WE / YOU DO
Find coordinates given slope
I DO
- Example 7, p. 191
WE DO
-√ Your Progress - p. 191 #7A
YOU DO
-√ Your Progress - p. 191 #7B
Practice
slope of a line
Demonstration of Learning p.192 #1-13
p. 192-195
- Rate of change from a table or graph
#14-19
- Slope of a line passing through 2 points
#20 – 31; 36 - 39, 62
- Find coordinates given slope
#32-35; 44-47
- Applications
#48-57
Big Idea: Linear Functions and Patterns
Objective: The student will learn how to
write and graph a linear function in slopeintercept form.
Common Core Mathematics Standard 2
38
Write & graph linear functions
Read GET READY for the Lesson, p. 204
Does the line have a positive slope or negative slope?
What do x and y represent in the equation?
A checking plan offered by a bank includes a $10
monthly service fee and a $0.20 per check fee for
accounts with an average daily balance of less
than $2000. What equation describes this plan?
Vocabulary
Write & graph linear functions
Slope intercept form of a
linear equation
𝒚 = 𝒎𝒙 + 𝒃
where m is the slope and b
is the y-intercept
(0, b)
O
y = mx + b
I / WE / YOU
Write & graph linear functions
I / WE DO
Example 1, p. 204
YOU DO
-√ Your Progress - p. 204 #1
I / WE / YOU
Write & graph linear functions
I / WE DO
Example 2, p. 205
YOU DO
-√ Your Progress - p. 205 #2
I / WE / YOU
I DO
- Example 3, p. 205
WE DO
-√ Your Progress - p. 205 #3A
WE DO
-√ Your Progress - p. 205 #3C
YOU DO
-√ Your Progress - p. 205 #3B
YOU DO
-√ Your Progress - p. 205 #3D
Write & graph linear functions
Vocabulary
Starting point
Rate of change
Write & graph linear functions
The y- intercept of a
linear equation that
models real-world data.
The slope of a linear
equation that models real
world data.
I / WE / YOU
Write & graph linear functions
I / WE DO
Example 4, p. 206
YOU DO
-√ Your Progress - p. 206 #4
Practice
Write & graph linear functions
p. 207 - 208
- Write a linear function given slope and y-intercept
#11 – 17, 39 - 44
- Write a linear function given a graph
#18 – 23
- Graph a linear function given an equation.
#24 – 32
- Applications
#33 -38
Big Idea: Linear Functions and Patterns
Objective: The student will learn how to
write a linear function and use it to solve
problems.
Common Core Mathematics Standard 2
47
Linear functions
Read GET READY for the Lesson, p. 213
How do you know that the slope is 7000?
A biologist is studying how fast a bacteria
grows. The population of bacteria has an
average growth of 200 bacteria per hour.
Describe the graph that demonstrates the
growth.
I / WE / YOU
I / WE DO
- Example 1, p. 213
YOU DO
-√ Your Progress - p. 213 #1
Linear functions
I / WE / YOU
I / WE DO
- Example 2, p. 214
YOU DO
-√ Your Progress - p.214 #2
Linear functions
I / WE / YOU
I / WE DO
- Example 3, p. 215
YOU DO
-√ Your Progress - p.215 #3
Linear functions
I / WE / YOU
I / WE DO
- Example 4, p. 216
YOU DO
-√ Your Progress - p.216 #4
Linear functions
RECALL - Vocabulary
Standard form of a
linear equation
Linear functions
𝑨𝒙 + 𝑩𝒚 = 𝑪
I / WE / YOU
I / WE DO
- Example 3, p. 221
YOU DO
-√ Your Progress - p.221 #3
Linear functions
RECALL Vocabulary Write & graph linear functions
Slope intercept form of a
linear equation
𝒚 = 𝒎𝒙 + 𝒃
where m is the slope and b
is the y-intercept
(0, b)
O
y = mx + b
I / WE / YOU
I / WE DO
- Example 4, p. 221
YOU DO
-√ Your Progress - p.221 #4
Linear functions
Practice
Demonstration of Learning – p. 216 #1-9
Linear functions
- Write a linear function given a point and the slope
p. 217 #10 – 17; p. 223 # 12 – 17
- Write a linear function given 2 points
p. 217 #18 – 25; 30 – 35
- Write a linear function in standard form
p. 223 #20 – 27
- Write a linear function in slope-intercept form
p. 223 #28 – 35
- Application
p. 217 #8, 9, 26 – 29; p. 224 #37, 38, 40, 41
Big Idea: Linear Functions and Patterns
Objective: The student will learn how
use lines of best fit to make and evaluate
predictions.
Common Core Mathematics Standard 2
58
Lines of best fit
Read GET READY for the Lesson, p. 227
Does the line have positive or negative slope?
How do you know?
What would you do to find the equation of that
line?
Vocabulary
Scatter plot
Lines of best fit
A graph in which two sets
of data are plotted as
ordered pairs .
Used to investigate a
relationship between two
quantities.
Lines of best fit
Vocabulary
Scatter plot with a
positive correlation
positive slope
O
Lines of best fit
Vocabulary
Scatter plot with a
negative correlation
negative slope
O
Lines of best fit
Vocabulary
Scatter plot with no
correlation
O
I / WE / YOU
I / WE DO
- Example 1, p. 227
YOU DO
-√ Your Progress - p. 228 #1
Lines of best fit
Algebra LAB p. 228
Lines of best fit
Is there a relationship between the length of a person’s
foot and their height?
Make a prediction. What do you think the
relationship between the length of person’s foot and
their height is?
Describe the relationship between the length of a
person’s foot and their height in terms of independent
and dependent variables.
Algebra LAB p. 228
Foot length (cm)
Height (cm)
Lines of best fit
Foot length (cm)
Height (cm)
I / WE / YOU
I / WE DO
- Example 2, p. 229
- Example 3, p. 230
YOU DO
-√ Your Progress - p. 229 #2
- √ Your Progress - p. 230 #3
Lines of best fit
Practice
Lines of best fit
- Demonstration of Learning p. 230 #1 -7
- Application
p. 231 – 232 #8 - 27