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

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 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 (3, 2) Ordered pair (x, y) Origin : (0, 0) Horizontal axis : x-axis

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 - 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

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 Graph using intercepts Linear equation Standard form of a linear equation The equation of a straight line 𝑨𝒙+𝑩𝒚=𝑪

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) (0, 4) x-intercept : (x, 0) (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 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

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 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 𝒄𝒉𝒂𝒏𝒈𝒆 𝒊𝒏 𝒚 𝒄𝒉𝒂𝒏𝒈𝒆 𝒊𝒏 𝒙

The table on p.187 shows the distance a person has walked for various amounts of time rate of change = This means that the person walked 4 feet per second Slope of a line 𝒄𝒉𝒂𝒏𝒈𝒆 𝒊𝒏 𝒚 𝒄𝒉𝒂𝒏𝒈𝒆 𝒊𝒏 𝒙 𝒄𝒉𝒂𝒏𝒈𝒆 𝒊𝒏 𝒅𝒊𝒔𝒕𝒂𝒏𝒄𝒆 𝒄𝒉𝒂𝒏𝒈𝒆 𝒊𝒏 𝒕𝒊𝒎𝒆 𝟒 𝒇𝒆𝒆𝒕 𝟏 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 = Slope of a line 𝒓𝒊𝒔𝒆 𝒓𝒖𝒏 (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 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 slope-intercept form. Common Core Mathematics Standard 2

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 Write & graph linear functions I DO - Example 3, p. 205 WE DO -√ Your Progress - p. 205 #3A -√ Your Progress - p. 205 #3C YOU DO -√ Your Progress - p. 205 #3B -√ 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 DO Example 4, p. 206 YOU DO -√ Your Progress - p. 206 #4

Practice Write & graph linear functions 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

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 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 𝑨𝒙+𝑩𝒚=𝑪

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 𝒚=𝒎𝒙+𝒃 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 functions Demonstration of Learning – p. 216 #1-9 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

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 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 positive slope O

Vocabulary Lines of best fit Scatter plot with a negative correlation negative slope O

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 fit Foot 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 Application p. 231 – 232 #8 - 27