6.4 Linear Function Date 11/05/18 Pick up your homework from back table. Copy down Essential Question. Work on Warm Up. Essential Question How is being linear different from non-linear? Warm Up: Answer the question Which one doesn’t belong (explain 2-3 sentences)

Review: Look for a pattern X -2 -1 1 2 3 4 5 Y 6 8 10 -4 -2 ∆𝒀=+2

Core Concept Linear function: a function that has a constant pattern (Rate of change). X -2 -1 1 2 3 4 5 Y 6 8 10 -4 -2 ∆𝒀=+2

Is this a linear function? X -2 -1 1 2 3 4 5 Y -6 7 11 13 17 ∆𝒀=𝐭𝐡𝐞𝐫𝐞 𝐢𝐬 𝐧𝐨𝐧𝐞

Core Concept NonLinear function: a function that has no constant pattern (Rate of change). X -2 -1 1 2 3 4 5 Y -6 7 11 13 17 ∆𝒀=𝐧𝐨𝐧𝐞

Identifying Functions from a Table

Identifying Functions from Graph

Core Concept If the exponent isn’t written, then it is a really 1

Identify Linear Equation Examples of linear equations. 𝑦=4 −3𝑥 𝑦=−3 4+𝑦 −4𝑥 Examples of nonlinear equations 𝑥𝑦+𝑥=2 𝑥 2 +𝑥𝑦+ 𝑦 2 For it to be a Linear Equation: No exponent greater than 1 Only variable is x and y

Determine Whether each equation is Linear

Determine Whether each equation is Linear

Determine whether the graph represents a linear or nonlinear function. 1. 2. 3. 4.

Determine whether the graph represents a linear or nonlinear function. 5. 6.

4.2 Slope Part 2 Date 11/06/18 Copy down Essential Question. Work on Warm Up. Essential Question Why is the rate of change the same as the slope? Warm Up: What does these 3 things have in common. 20 miles per hour 10 meters per second 4 dollars per pound

Core Concept

Review of Core Concept: Slope Slope is the rate of change between any points on a line. Slope is a ratio of change in the y to change in x. It is the measure of the steepness of the line.

Core Concept Review Change = Second value – first value Finding the pattern ( rate of change) Question: How do you go from 20 to 30? Equation: 20+ 𝑪𝒉𝒂𝒏𝒈𝒆 =30 Review the equation: 𝑪𝒉𝒂𝒏𝒈𝒆 =30−20 Change = Second value – first value

1. 2. 3. 4.

5. 4, −1 , (−2, −1) 6. 5, −3 , (5, 8)

Find the slope of a line that passes through each pair of points

4.2 Slope Part 3 Date 11/07/18 Copy down Essential Question. Work on Warm Up. Essential Question How does the slope affect the look of a function? Warm Up: Explain the joke

How steep is the steepest roller coaster? Ghost Rider Knott’s Berry Farm The Magnum Cedar Point, OH Superman 6 Flags Magic Mountain Xcelerator Knott’s Berry Farm These are completely vertical! Son of Beast King’s Island, OH How steep is the steepest roller coaster?

Imagine a roller coaster moving from LEFT to RIGHT

Find the Rate of Change from a Graph

Find the rate of change for each graph and tell me when it represent 1. 2. 𝑚= 9 𝐷𝑜𝑙𝑙𝑎𝑟𝑠 1 𝑆𝐻𝑖𝑟𝑡 or 9 Dollar per 1 shirt 𝑚= 72 𝑖𝑛. 𝐿𝑒𝑛𝑔𝑡ℎ 6 𝑖𝑛. 𝐻𝑖𝑒𝑔ℎ𝑡 or 12 in Length per 1 in. height

Find the rate of change for each graph and tell me when it represent The graph show your earning for babysitting

The graph shows the earnings of you and your friend for babysitting. Steepness is the dollar earn per hour of babysitting The friend got paid more with 28 dollar per 4 hours.

Application of Slope The diagram at the right shows the side view of a ski lift. What is the vertical change from: A to B? B to C? C to D? What is the horizontal change from: C to D 10 feet 40 feet 30 feet Which section is the steepest? B to C

A community theater performed a play each Saturday evening for 10 consecutive weeks. The graph shows the attendance for the performances in weeks 1, 4, 6, and 10. Describe the rates of change in attendance with respect to time. Week 1-4: Week 4-6: Week 6-10: increase of 99 people in attendance decrease of 22 people in attendance decrease of 148 people in attendance

The points in the table lie on a line. Find the slope of the line 1. ∆𝒙=+2 ∆𝒀=+8 m= ∆𝒀 ∆𝒙 m= 8 2

The points in the table lie on a line. Find the slope of the line 2. ∆𝒙=+5 ∆𝒀=+2 m= ∆𝒀 ∆𝒙 m= 2 5

The points in the table lie on a line. Find the slope of the line 3. ∆𝒙=+4 ∆𝒀=−𝟑 m= ∆𝒀 ∆𝒙 m= −3 4

4.3 Proportional Relationship Date 11/08/18 Copy down Essential Question. Work on Warm Up. Essential Question How can two things be in a proportional relationships Warm Up: Answer the question Which one doesn’t belong (explain 2-3 sentences)

Gulliver’s Travels was written by Jonathan Swift and published in 1726 Gulliver’s Travels was written by Jonathan Swift and published in 1726. Gulliver was ship wrecked on the island Lilliput, where the people were only 6 inches tall. When the Lillputians decide to make a shirt for Gulliver, a Lilliputian tailor stated that he could determine Gulliver’s measurements by simplifying measuring the distance around Gulliver’s Thumb. He said “ Twice around the thumb equals once around the wrist. Twice around the wrist is once around the neck. Twice around the neck is once around the waist”.

Translate the words into an equation t for Thumb, w for Wrist, n for Neck, x for Waist Twice around the thumb equals once around the wrist. 2𝑡=1𝑤 Twice around the wrist is once around the neck. 2𝑤=1𝑛 Twice around the neck is once around the waist”. 2𝑛=1𝑥

Using patterns fill in the chart

Graph the equation for the line.

Twice around the thumb equals once around the wrist. 𝑦=2𝑥 We call this a Proportional Relationship

Core Concept A relationship between two thing that has a constant slope ( rate of change or pattern). That passes through (0, 0)

1. CHARITY A professional soccer team is donating money to a local charity for each goal they score. Find the rate of change. Explain this is this a proportional relationship. 𝒎= 𝟕𝟓 𝑫𝒐𝒏𝒂𝒕𝒊𝒐𝒏 𝑫𝒐𝒍𝒍𝒂𝒓𝒔 𝟏 𝑵𝒖𝒎𝒃𝒆𝒓 𝒐𝒇 𝒈𝒐𝒂𝒍𝒔 𝒎=𝟕𝟓 𝒅𝒐𝒍𝒍𝒂𝒆𝒔 𝒑𝒆𝒓 𝟏 𝒈𝒐𝒂𝒍 𝑷𝒓𝒐𝒑𝒐𝒓𝒕𝒊𝒐𝒏𝒂𝒍 𝒃𝒆𝒄𝒂𝒖𝒔𝒆, 𝒊𝒕 𝒉𝒂𝒔 𝒂 𝒄𝒐𝒏𝒔𝒕𝒂𝒏𝒕 𝒔𝒍𝒐𝒑𝒆 𝒂𝒏𝒅 𝒑𝒂𝒔𝒔 𝒕𝒉𝒓𝒐𝒖𝒈𝒉 (𝟎,𝟎)

What do you think a Non-proportional relationship looks like?

Explain this is this a proportional relationship. GEOMETRY The table shows the perimeter of a square with sides of a given length. Find the rate of change. Explain this is this a proportional relationship. 𝒎= 𝟒 𝒊𝒏. 𝑷𝒆𝒓𝒊𝒎𝒆𝒕𝒆𝒓 𝟏 𝒊𝒏. 𝑺𝒊𝒅𝒆 𝑳𝒆𝒏𝒈𝒕𝒉 𝒎=𝟒 𝒊𝒏. 𝑷𝒆𝒓𝒊𝒎𝒆𝒕𝒆𝒓 𝒑𝒆𝒓 𝟏 𝒊𝒏. 𝒔𝒊𝒅𝒆𝒔 𝑷𝒓𝒐𝒑𝒐𝒓𝒕𝒊𝒐𝒏𝒂𝒍 𝒃𝒆𝒄𝒂𝒖𝒔𝒆, 𝒊𝒕 𝒉𝒂𝒔 𝒂 𝒄𝒐𝒏𝒔𝒕𝒂𝒏𝒕 𝒔𝒍𝒐𝒑𝒆 𝒂𝒏𝒅 𝒑𝒂𝒔𝒔 𝒕𝒉𝒓𝒐𝒖𝒈𝒉 (𝟎,𝟎)

Tell whether x and y are in a proportional relationship Tell whether x and y are in a proportional relationship. Explain your reasoning. If so, write an equation that represents the relationship. 1. 2. Proportional, Has a constant slope and does go through (0,0) Not Proportional, does go through (0,0)

Has a constant slope and does go through (0,0) Not Proportional, Tell whether x and y are in a proportional relationship. Explain your reasoning. If so, write an equation that represents the relationship. 3. 4. ∆𝒙=+3 x 3 6 9 12 y 1 2 4 ∆𝒀=+1 Proportional, Has a constant slope and does go through (0,0) Not Proportional, does not have constant slope

Lesson Closure: Math Talk

4.4 Slope-Intercept Form Date 11/09/18 Turn in your homework to back table Copy down Essential Question. Work on Warm Up. Essential Question How do you graph using a slope and y-intercept? Warm Up: Draw and label the slope

Core Concept

Core Concept Review : Find slope ∆𝒙=+1 m= ∆𝒀 ∆𝒙 X -2 -1 1 2 3 4 5 Y 8 11 14 17 ∆𝒀=+3 m= 𝟑 𝟏

Core Concept Review: Find Y-intercept X -2 -1 1 2 3 4 5 Y 8 11 14 17 -4 -1 2 b=2

Core Concept Review: Find Y-intercept m= 𝟑 𝟏 b=2 X -2 -1 1 2 3 4 5 Y 8 11 14 17 -4 -1 2 y = mx + b y = 𝟑 𝟏 x + 2

𝒚= 𝟏 𝟐 𝒙+𝟏 𝒚= −𝟐 𝟓 𝒙−𝟏