Unit 3 Linear Functions and Patterns
2
Big Idea: Linear Functions and Patterns
Objective: The student will learn how to interpret graphs
Common Core Mathematics Standard 2
Interpret graphsRead 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 Interpret graphs
function A relation between input and output.
In a function, the output depends on the input.
Vocabulary Interpret graphs
Coordinate system Used to graph a function
Formed by the intersection of two number lines, the horizontal axis and vertical axis
Vocabulary Interpret graphs
Coordinate system Used to graph a function
Formed by the intersection of two number lines, the horizontal axis and vertical axis
Vocabulary Interpret graphs
Vertical axis : y-axis
Horizontal axis : x-axis
Origin : (0, 0)
Ordered pair(x, y)(3, 2)
I / WE / YOU DO Interpret graphs
I / WE DO- Example 1, p. 53
YOU DO-√ Your Progress, p. 53 #1
Vocabulary Interpret graphs
In the example the blood flow depends on the number of days since the injury.
Independent variable
Dependent variable
The number of days since the injury
The percent of normal blood flow
I / WE / YOU DO Interpret graphs
I DO- Example 2, p. 54
WE DO- √ Your Progress - p.54 #2A
YOU DO - √ Your Progress - p.54 #2B
I / WE / YOU DO Interpret graphs
I / WE DO-Example 3, p. 54
YOU DO-√ Your Progress - p.54 #3
I / WE / YOU DO Interpret graphs
I / WE DO-Example 4, p. 55
YOU DO-√ Your Progress - p.55 #4
Practice Interpret graphs
Demonstration of learning – p. 56 # 1 - 7p. 56-58 # 10 - 21
14
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
Graph using interceptsRead 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 Graph using intercepts
Linear equation
Standard form of a linear equation
The equation of a straight line
I / WE / YOU DO Graph using intercepts
I DO- Example 1, p. 155
WE DO-√ Your Progress - p. 156 #1A
YOU DO-√ Your Progress - p. 156 #1B
Vocabulary Graph using intercepts
X-intercept
y-intercept
The x-coordinate of the point where the graph of an equation crosses the x-axis
The y-coordinate of the point where the graph of an equation crosses the y-axis.
Vocabulary Graph using intercepts
y-intercept : (0, y)
x-intercept : (x, 0)
(0, 4)
(3, 0)
I / WE / YOU DO Graph using intercepts
I DO-Example 2, p. 156
WE DO-√ Your Progress - p. 156 #2A
YOU DO-√ Your Progress - p. 156 #2B
I / WE / YOU DO Graph using intercepts
I / WE DO-Example 3, p. 157
YOU DO-√ Your Progress - p. 157 #3
I / WE / YOU DO Graph using intercepts
I DO-Example 4, p. 157
WE DO-√ Your Progress - p. 157 #4A
YOU DO-√ Your Progress - p. 157 #4B
I / WE / YOU DO Graph using intercepts
I / WE DO-Example 5, p. 158
YOU DO-√ Your Progress - p. 158 #5
Practice Graph using interceptsDemonstration of Learning – p. 158 # 1 - 11p. 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
25
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
Slope of a lineRead 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 Slope of a line
Rate of change
rate of change =
A ratio that describes, on average, how much one quantity changes with respect to another quantity
Slope of a lineThe table on p.187 shows the distance a person has walked for various amounts of time
rate of change =
rate of change =
rate of change =
This means that the person walked 4 feet per second
I / WE / YOU DO Slope of a line
I DO-Example 1, p. 187
WE DO-√ Your Progress - p. 188 #1A
YOU DO-√ Your Progress - p. 188 #1B
I / WE / YOU DO Slope of a line
I / WE DO-Example 2, p. 188
YOU DO-√ Your Progress - p. 188 #2
Slope of a line
slope =
(4, 5)
(1, 3)
I / WE / YOU DO Positive slope of a line
I DO- Example 3, p. 190
WE DO-√ Your Progress - p. 190 #3A
YOU DO-√ Your Progress - p. 190 #3B
I / WE / YOU DO Negative slope of a line
I DO- Example 4, p. 190
WE DO-√ Your Progress - p. 190 #4A
YOU DO-√ Your Progress - p. 190 #4B
I / WE / YOU DO Zero slope of a line
I DO- Example 5, p. 190
WE DO-√ Your Progress - p. 190 #5A
YOU DO-√ Your Progress - p. 190 #5B
I / WE / YOU DO Undefined slope of a line
I DO- Example 6, p. 191
WE DO-√ Your Progress - p. 191 #6A
YOU DO-√ Your Progress - p. 191 #6B
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 lineDemonstration of Learning p.192 #1-13p. 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
38
Big Idea: Linear Functions and Patterns
Objective: The student will learn how to write and graph a linear function in slope-intercept form.
Common Core Mathematics Standard 2
Write & graph linear functionsRead 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
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 DOExample 1, p. 204
YOU DO-√ Your Progress - p. 204 #1
I / WE / YOU Write & graph linear functions
I / WE DOExample 2, p. 205
YOU DO-√ Your Progress - p. 205 #2
I / WE / YOU Write & graph linear functions
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
Vocabulary Write & graph linear functions
Starting point
Rate of change
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 DOExample 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
47
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
Linear functionsRead 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 Linear functions
I / WE DO- Example 1, p. 213
YOU DO-√ Your Progress - p. 213 #1
I / WE / YOU Linear functions
I / WE DO- Example 2, p. 214
YOU DO-√ Your Progress - p.214 #2
I / WE / YOU Linear functions
I / WE DO- Example 3, p. 215
YOU DO-√ Your Progress - p.215 #3
I / WE / YOU Linear functions
I / WE DO- Example 4, p. 216
YOU DO-√ Your Progress - p.216 #4
RECALL - Vocabulary Linear functions
Standard form of a linear equation
I / WE / YOU Linear functions
I / WE DO- Example 3, p. 221
YOU DO-√ Your Progress - p.221 #3
RECALL Vocabulary Write & graph linear functions
Slope intercept form of a linear equation
where m is the slope and b is the
y-intercept
(0, b)
O
y = mx + b
I / WE / YOU Linear functions
I / WE DO- Example 4, p. 221
YOU DO-√ Your Progress - p.221 #4
Practice Linear functionsDemonstration of Learning – p. 216 #1-9
- Write a linear function given a point and the slopep. 217 #10 – 17; p. 223 # 12 – 17
- Write a linear function given 2 pointsp. 217 #18 – 25; 30 – 35
- Write a linear function in standard formp. 223 #20 – 27
- Write a linear function in slope-intercept formp. 223 #28 – 35
- Applicationp. 217 #8, 9, 26 – 29; p. 224 #37, 38, 40, 41
58
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
Lines of best fitRead 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 Lines of best fit
Scatter plot A graph in which two sets of data are plotted as ordered pairs .
Used to investigate a relationship between two quantities.
Vocabulary Lines of best fit
Scatter plot with a positive correlation
O
positive slope
Vocabulary Lines of best fit
Scatter plot with a negative correlation
O
negative slope
Vocabulary Lines of best fit
Scatter plot with no correlation
O
I / WE / YOU Lines of best fit
I / WE DO- Example 1, p. 227
YOU DO-√ Your Progress - p. 228 #1
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 Lines of best fitFoot length (cm) Height (cm) Foot length (cm) Height (cm)
I / WE / YOU Lines of best fit
I / WE DO- Example 2, p. 229- Example 3, p. 230
YOU DO-√ Your Progress - p. 229 #2- √ Your Progress - p. 230 #3
Practice Lines of best fit
- Demonstration of Learning p. 230 #1 -7
- Applicationp. 231 – 232 #8 - 27