# Algebra 2 Chapter 5 Resource Book Answer Key - mcdougal

Download presentationWe think you have liked this presentation. If you wish to download it, please recommend it to your friends in any social system. Share buttons are a little bit lower. Thank you!Buttons: Presentation is loading. Please wait.Published byJune Butler Modified over 2 years ago 1 Section 9B Linear ModelingPages { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "http://slideplayer.com/6137588/18/images/1/Section+9B+Linear+Modeling.jpg", "name": "Section 9B Linear Modeling", "description": "Pages 542-553.", "width": "800" } 2 9-B Linear Functions A linear function has a constant rate of change and a straight-line graph. old example: The initial population of Straightown is 10, 000 and increases by 500 people per year. Independent variable: year Dependent variable: population Population is a function of time(year). The constant rate of change is 500 people per year. { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "http://slideplayer.com/6137588/18/images/2/9-B+Linear+Functions.+A+linear+function+has+a+constant+rate+of+change+and+a+straight-line+graph..jpg", "name": "9-B Linear Functions. A linear function has a constant rate of change and a straight-line graph.", "description": "old example: The initial population of Straightown is 10, 000 and increases by 500 people per year. Independent variable: year. Dependent variable: population. Population is a function of time(year). The constant rate of change is 500 people per year.", "width": "800" } 3 old example: The initial population of Straightown is 10, 000 and increases by 500 people per year.Graph Data Table Year Straightown 10,000 5 12,500 10 15,000 15 17,500 20 20,000 40 30,000 Equation P = 10, x t { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "http://slideplayer.com/6137588/18/images/3/old+example%3A+The+initial+population+of+Straightown+is+10%2C+000+and+increases+by+500+people+per+year..jpg", "name": "old example: The initial population of Straightown is 10, 000 and increases by 500 people per year.", "description": "Graph. Data Table. Year. Straightown. 10,000. 5. 12,500. 10. 15,000. 15. 17,500. 20. 20,000. 40. 30,000. Equation. P = 10,000 + 500 x t.", "width": "800" } 4 We define rate of change of a linear function by:where (x1,y1) and (x2,y2) are any two ordered pairs of the function. { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "http://slideplayer.com/6137588/18/images/4/We+define+rate+of+change+of+a+linear+function+by%3A.jpg", "name": "We define rate of change of a linear function by:", "description": "where (x1,y1) and (x2,y2) are any two ordered pairs of the function.", "width": "800" } 5 Rate of change is ALWAYS 500 (people per year).old example: The initial population of Straightown is 10, 000 and increases by 500 people per year. Year Straightown 10,000 5 12,500 10 15,000 15 17,500 20 20,000 40 30,000 = 500 = 500 = 500 = 500 Rate of change is ALWAYS 500 (people per year). { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "http://slideplayer.com/6137588/18/images/5/Rate+of+change+is+ALWAYS+500+%28people+per+year%29..jpg", "name": "Rate of change is ALWAYS 500 (people per year).", "description": "old example: The initial population of Straightown is 10, 000 and increases by 500 people per year. Year. Straightown. 10,000. 5. 12,500. 10. 15,000. 15. 17,500. 20. 20,000. 40. 30,000. = 500. = 500. = 500. = 500. Rate of change is ALWAYS 500 (people per year).", "width": "800" } 6 We define slope of a straight line by:where (x1,y1) and (x2,y2) are any two points on the graph of the straight line. { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "http://slideplayer.com/6137588/18/images/6/We+define+slope+of+a+straight+line+by%3A.jpg", "name": "We define slope of a straight line by:", "description": "where (x1,y1) and (x2,y2) are any two points on the graph of the straight line.", "width": "800" } 7 { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "http://images.slideplayer.com/18/6137588/slides/slide_8.jpg", "name": "", "description": "", "width": "800" } 8 { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "http://images.slideplayer.com/18/6137588/slides/slide_9.jpg", "name": "", "description": "", "width": "800" } 9 Postage cost (dependent) 1 oz $0.37 2 oz $0.60 3 oz $0.83 4 oz $1.06 9-B Example: The table below gives the cost of US mail based on weight. What is the rate of change? Graph the cost as a function of weight and determine the slope. Weight (independent) Postage cost (dependent) 1 oz $0.37 2 oz $0.60 3 oz $0.83 4 oz $1.06 5 oz $1.29 6 oz $1.52 7 oz $1.75 Rate of change is ALWAYS 0.23 (dollars per ounce). { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "http://slideplayer.com/6137588/18/images/9/Postage+cost+%28dependent%29+1+oz+%240.37+2+oz+%240.60+3+oz+%240.83+4+oz+%241.06.jpg", "name": "Postage cost (dependent) 1 oz $0.37 2 oz $0.60 3 oz $0.83 4 oz $1.06", "description": "9-B. Example: The table below gives the cost of US mail based on weight. What is the rate of change Graph the cost as a function of weight and determine the slope. Weight (independent) Postage cost (dependent) 1 oz. $0.37. 2 oz. $0.60. 3 oz. $0.83. 4 oz. $1.06. 5 oz. $1.29. 6 oz. $1.52. 7 oz. $1.75. Rate of change is ALWAYS 0.23 (dollars per ounce).", "width": "800" } 10 Rate of change is $0.23 per oz.9-B Example: The table below gives the cost of US mail based on weight. What is the rate of change? Graph the cost as a function of weight and determine the slope. Weight Postage cost Difference 1 oz $0.37 2 oz $0.60 $0.23 3 oz $0.83 4 oz $1.06 5 oz $1.29 6 oz $1.52 7 oz $1.75 Rate of change is $0.23 per oz. { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "http://slideplayer.com/6137588/18/images/10/Rate+of+change+is+%240.23+per+oz..jpg", "name": "Rate of change is $0.23 per oz.", "description": "9-B. Example: The table below gives the cost of US mail based on weight. What is the rate of change Graph the cost as a function of weight and determine the slope. Weight. Postage cost. Difference. 1 oz. $0.37. 2 oz. $0.60. $0.23. 3 oz. $0.83. 4 oz. $1.06. 5 oz. $1.29. 6 oz. $1.52. 7 oz. $1.75. Rate of change is $0.23 per oz.", "width": "800" } 11 9-B Example: The table below gives the cost of US mail based on weight. What is the rate of change? Graph the cost as a function of weight and determine the slope. { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "http://slideplayer.com/6137588/18/images/11/9-B.jpg", "name": "9-B", "description": "Example: The table below gives the cost of US mail based on weight. What is the rate of change Graph the cost as a function of weight and determine the slope.", "width": "800" } 12 9-B Example: The table below gives the cost of US mail based on weight. What is the rate of change? Graph the cost as a function of weight and determine the slope. { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "http://slideplayer.com/6137588/18/images/12/9-B.jpg", "name": "9-B", "description": "Example: The table below gives the cost of US mail based on weight. What is the rate of change Graph the cost as a function of weight and determine the slope.", "width": "800" } 13 9-B Example: The table below gives the cost of US mail based on weight. What is the rate of change? Graph the cost as a function of weight and determine the slope. { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "http://slideplayer.com/6137588/18/images/13/9-B.jpg", "name": "9-B", "description": "Example: The table below gives the cost of US mail based on weight. What is the rate of change Graph the cost as a function of weight and determine the slope.", "width": "800" } 14 9-B Example: The table below gives the cost of US mail based on weight. What is the rate of change? Graph the cost as a function of weight and determine the slope. { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "http://slideplayer.com/6137588/18/images/14/9-B.jpg", "name": "9-B", "description": "Example: The table below gives the cost of US mail based on weight. What is the rate of change Graph the cost as a function of weight and determine the slope.", "width": "800" } 15 For linear functions: Slope = Rate of Change Use any two ordered pairs (points on the graph) to calculate rate of change (slope). { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "http://slideplayer.com/6137588/18/images/15/For+linear+functions%3A+Slope+%3D+Rate+of+Change..jpg", "name": "For linear functions: Slope = Rate of Change.", "description": "Use any two ordered pairs (points on the graph) to calculate rate of change (slope).", "width": "800" } 16 How does rate of change (slope) affect steepness…9-B …the greater the rate of change (slope), the steeper the graph. { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "http://slideplayer.com/6137588/18/images/16/How+does+rate+of+change+%28slope%29+affect+steepness%E2%80%A6.jpg", "name": "How does rate of change (slope) affect steepness…", "description": "9-B. …the greater the rate of change (slope), the steeper the graph.", "width": "800" } 17 Independent variable: price Dependent variable: demand (of pineapples) ex2/545 A linear function is used to describe how the demand for pineapples varies with the price. We know at a price of $2, the demand is 80 pineapples and at a price of $5, the demand is 50 pineapples. Find the rate of change (slope) for this function and then graph the function Independent variable: price Dependent variable: demand (of pineapples) Demand is a function of price. ($2,80) and ($5,50) { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "http://slideplayer.com/6137588/18/images/17/Independent+variable%3A+price+Dependent+variable%3A+demand+%28of+pineapples%29.jpg", "name": "Independent variable: price Dependent variable: demand (of pineapples)", "description": "ex2/545 A linear function is used to describe how the demand for pineapples varies with the price. We know at a price of $2, the demand is 80 pineapples and at a price of $5, the demand is 50 pineapples. Find the rate of change (slope) for this function and then graph the function. Independent variable: price. Dependent variable: demand (of pineapples) Demand is a function of price. ($2,80) and ($5,50)", "width": "800" } 18 ($2, 80 pineapples) and ($5, 50 pineapples)9-B ex2/545 A linear function is used to describe how the demand for pineapples varies with the price. We know at a price of $2, the demand is 80 pineapples and at a price of $5, the demand is 50 pineapples. Find the rate of change (slope) for this function and then graph the function ($2, 80 pineapples) and ($5, 50 pineapples) For every dollar increase in price, the demand for pineapples decreases by 10. { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "http://slideplayer.com/6137588/18/images/18/%28%242%2C+80+pineapples%29+and+%28%245%2C+50+pineapples%29.jpg", "name": "($2, 80 pineapples) and ($5, 50 pineapples)", "description": "9-B. ex2/545 A linear function is used to describe how the demand for pineapples varies with the price. We know at a price of $2, the demand is 80 pineapples and at a price of $5, the demand is 50 pineapples. Find the rate of change (slope) for this function and then graph the function. ($2, 80 pineapples) and ($5, 50 pineapples) For every dollar increase in price, the demand for pineapples decreases by 10.", "width": "800" } 19 ($2, 80 pineapples) and ($5, 50 pineapples).9-B ex2/545 A linear function is used to describe how the demand for pineapples varies with the price. We know at a price of $2, the demand is 80 pineapples and at a price of $5, the demand is 50 pineapples. Find the rate of change (slope) for this function and then graph the function ($2, 80 pineapples) and ($5, 50 pineapples). For every dollar increase in price, the demand for pineapples decreases by 10. { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "http://slideplayer.com/6137588/18/images/19/%28%242%2C+80+pineapples%29+and+%28%245%2C+50+pineapples%29..jpg", "name": "($2, 80 pineapples) and ($5, 50 pineapples).", "description": "9-B. ex2/545 A linear function is used to describe how the demand for pineapples varies with the price. We know at a price of $2, the demand is 80 pineapples and at a price of $5, the demand is 50 pineapples. Find the rate of change (slope) for this function and then graph the function. ($2, 80 pineapples) and ($5, 50 pineapples). For every dollar increase in price, the demand for pineapples decreases by 10.", "width": "800" } 20 ($2, 80 pineapples) and ($5, 50 pineapples).9-B ($2, 80 pineapples) and ($5, 50 pineapples). For every dollar increase in price, the demand for pineapples decreases by 10. { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "http://slideplayer.com/6137588/18/images/20/%28%242%2C+80+pineapples%29+and+%28%245%2C+50+pineapples%29..jpg", "name": "($2, 80 pineapples) and ($5, 50 pineapples).", "description": "9-B. ($2, 80 pineapples) and ($5, 50 pineapples). For every dollar increase in price, the demand for pineapples decreases by 10.", "width": "800" } 21 For linear functions: Slope = Rate of Change Use any two ordered pairs (points on the graph) to calculate rate of change (slope). Postive Slope Negative Slope { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "http://slideplayer.com/6137588/18/images/21/For+linear+functions%3A+Slope+%3D+Rate+of+Change.+Use+any+two+ordered+pairs+%28points+on+the+graph%29+to+calculate+rate+of+change+%28slope%29..jpg", "name": "For linear functions: Slope = Rate of Change. Use any two ordered pairs (points on the graph) to calculate rate of change (slope).", "description": "Postive Slope. Negative Slope.", "width": "800" } 22 The Rate of Change Rule (page546)9-B The Rate of Change Rule (page546) change in dependent variable = (rate of change) x (change in independent variable) ex3/545 Predict the change in demand for pineapples if the price increases by $3. change in demand = (-10 pineapples per dollar) x $ = pineapples If the price of pineapples increases by $3, then the demand will decrease by 30 pineapples { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "http://slideplayer.com/6137588/18/images/22/The+Rate+of+Change+Rule+%28page546%29.jpg", "name": "The Rate of Change Rule (page546)", "description": "9-B. The Rate of Change Rule (page546) change in dependent variable = (rate of change) x (change in independent variable) ex3/545 Predict the change in demand for pineapples if the price increases by $3. change in demand = (-10 pineapples per dollar) x $3 = -30 pineapples. If the price of pineapples increases by $3, then the demand will decrease by 30 pineapples.", "width": "800" } 23 More Practice 17/554 The water depth in a reservoir decreases at a rate of 0.25 inch per hour because of evaporation. How much does the water depth change in 6.5 hours? 19/554 A tree increases its diameter by 0.2 inches per year by adding annual rings. How much does the diameter of the tree increase in 4.5 years? { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "http://slideplayer.com/6137588/18/images/23/More+Practice.jpg", "name": "More Practice", "description": "17/554 The water depth in a reservoir decreases at a rate of 0.25 inch per hour because of evaporation. How much does the water depth change in 6.5 hours 19/554 A tree increases its diameter by 0.2 inches per year by adding annual rings. How much does the diameter of the tree increase in 4.5 years", "width": "800" } 24 9-B General Equation for a Linear Function dependent = initial value + (rate of change x independent) or y = m x + b where m is slope and b is y intercept. { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "http://slideplayer.com/6137588/18/images/24/9-B.jpg", "name": "9-B", "description": "General Equation for a Linear Function dependent = initial value + (rate of change x independent) or y = m x + b where m is slope and b is y intercept.", "width": "800" } 25 General Equation for a Linear FunctionStraightown Population: m = 500 and initial value = 10000 P = t [ Y = x ] Pineapple Demand: m = -10 and initial value = 100 D = 100 – 10p [ Y = 100 – 10x ] { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "http://slideplayer.com/6137588/18/images/25/General+Equation+for+a+Linear+Function.jpg", "name": "General Equation for a Linear Function", "description": "Straightown Population: m = 500 and initial value = 10000. P = 10000 + 500t. [ Y = 10000 + 500x ] Pineapple Demand: m = -10 and initial value = 100. D = 100 – 10p. [ Y = 100 – 10x ]", "width": "800" } 26 More Practice 23/555 The price of a particular model car is $12,000 today and rises with time at a constant rate of $1200 per year. A) Clearly identify independent and dependent variable. B) Find a linear equation to describe the situation. C) How much will a new car cost in 2.5 years. 25/555 A snowplow has a maximum speed of 30 miles per hour on a dry highway. Its maximum speed decreases by 0.5 miles per hour for every inch of snow on the highway. A) Clearly identify independent and dependent variable. B) Find a linear equation to describe the situation. C) At what snow depth will the snowplow be unable to move? 27/555 You can rent time on computers at the local copy center for $5 setup charge and an additional $3 for every 5 minutes. A) Clearly identify independent and dependent variable. B) Find a linear equation to describe the situation. C) How much time can you rent for $15? { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "http://slideplayer.com/6137588/18/images/26/More+Practice.jpg", "name": "More Practice", "description": "23/555 The price of a particular model car is $12,000 today and rises with time at a constant rate of $1200 per year. A) Clearly identify independent and dependent variable. B) Find a linear equation to describe the situation. C) How much will a new car cost in 2.5 years. 25/555 A snowplow has a maximum speed of 30 miles per hour on a dry highway. Its maximum speed decreases by 0.5 miles per hour for every inch of snow on the highway. A) Clearly identify independent and dependent variable. B) Find a linear equation to describe the situation. C) At what snow depth will the snowplow be unable to move 27/555 You can rent time on computers at the local copy center for $5 setup charge and an additional $3 for every 5 minutes. A) Clearly identify independent and dependent variable. B) Find a linear equation to describe the situation. C) How much time can you rent for $15", "width": "800" } 27 More Practice 29/555 Suppose that you were 20 inches long at birth and 4 feet tall on your tenth birthday. A) Clearly identify independent and dependent variable. B) Find a linear equation to describe the situation. C) Use the equation to predict your height at ages 2,6,20,50. D) Comment on the validity of the model. 31/555 A YMCA fundraiser offers raffle tickets for $5 each. The prize for the raffle is a $350 television set, which must be purchased with proceeds from the ticket sales. Find an equation that gives the profit/loss for the raffle as it varies with the number of tickets sold. How many tickets must be sold for the raffle sales to equal the cost of the prize? 33/555 A $1000 washing machine is depreciated for tax purposes at a rate of $50 per year. Find an equation for the depreciated value of the washing machine as it varies with time. When does the depreciated value reach $0? { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "http://slideplayer.com/6137588/18/images/27/More+Practice.jpg", "name": "More Practice", "description": "29/555 Suppose that you were 20 inches long at birth and 4 feet tall on your tenth birthday. A) Clearly identify independent and dependent variable. B) Find a linear equation to describe the situation. C) Use the equation to predict your height at ages 2,6,20,50. D) Comment on the validity of the model. 31/555 A YMCA fundraiser offers raffle tickets for $5 each. The prize for the raffle is a $350 television set, which must be purchased with proceeds from the ticket sales. Find an equation that gives the profit/loss for the raffle as it varies with the number of tickets sold. How many tickets must be sold for the raffle sales to equal the cost of the prize 33/555 A $1000 washing machine is depreciated for tax purposes at a rate of $50 per year. Find an equation for the depreciated value of the washing machine as it varies with time. When does the depreciated value reach $0", "width": "800" } 28 Linear Functions Constant Rate of Change Straight Line GraphDependent = Initial + Rate x Independent Y = mX + b { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "http://slideplayer.com/6137588/18/images/28/Linear+Functions+Constant+Rate+of+Change+Straight+Line+Graph.jpg", "name": "Linear Functions Constant Rate of Change Straight Line Graph", "description": "Dependent = Initial + Rate x Independent. Y = mX + b.", "width": "800" } 29 9-B Homework: Pages # 12a-b, 14a-b, 18, 20, 24, 26, 28, 32 { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "http://slideplayer.com/6137588/18/images/29/9-B+Homework%3A+Pages+553-555+%23+12a-b%2C+14a-b%2C+18%2C+20%2C+24%2C+26%2C+28%2C+32.jpg", "name": "9-B Homework: Pages 553-555 # 12a-b, 14a-b, 18, 20, 24, 26, 28, 32", "description": "9-B Homework: Pages 553-555 # 12a-b, 14a-b, 18, 20, 24, 26, 28, 32", "width": "800" } Ppt on historical places in delhi Ppt on ideal gas laws Ppt online shopping project proposal Ppt on north india mountains Ppt on buildings paintings and books Ppt on channels of distribution powerpoint Ppt on natural resources and conservation major Ppt on relays and circuit breakers Ppt on social media and social networking Ppt on image fusion Section 9B Linear Modeling Pages Linear Functions 9-B A linear function describes a relation between independent (input) and dependent (output)Section 9B Linear ModelingSection 9B Linear Modeling Pages Linear Modeling 9-B LINEAR constant rate of change.Section 9B Linear Modeling Pages Linear Functions A Linear Function changes by the same absolute amount for each unit of change in the input.Copyright © 2011 Pearson Education, Inc. Modeling Our World 9A Discussion Paragraph 1 web 39. Daylight Hours 40. Variable Tables 1 world 41. Everyday.Copyright © 2011 Pearson Education, Inc. Modeling Our World.Objective - To graph linear equations using the slope and y-intercept.2.4 Using Linear Models. Slope is “rate of change” Examples: Look for KEY words! 23 miles per gallon 20 gallons/second 3 inches each year $3 a ticket.5.2 Linear relationships. Weight of objects Create a scatter plot Linear relationship: when the points in a scatter plot lie along a straight line. Is. P – 60 5ths APPLY LINEAR FUNCTIONS X-axis time since purchase Y-axis value Use two intercepts (0, initial value) and (time until value. Start with the average of 20 and 40. Subtract the number of inches in two feet. Take 50% of your answer. Square your result Multiply by the degree.ADVANCED TRIG Page 90 is due today, any questions?Why use it? Data ysis, Make Predictions, Determine best value, sale price, or make various consumer decisions.WHAT YOU’LL LEARN: Finding rates of change from tables and graphs. AND WHY: To find rates of change in real- world situations, such as the rate of descent.Representing Linear PatternsWarm Up A school club pays $35.75 to rent a video cassette player to show a movie for a fund raising project. The club charges 25 cents per ticket for.Speed Key Question: Investigation 4AUnit 1 – First-Degree Equations and InequalitiesWrite linear equations from tables by identifying the rate of change and the initial value.Review Videos Graphing the x and y intercept Graphing the x and y intercepts Graphing a line in slope intercept form Converting into slope intercept form. Similar presentations © 2017 SlidePlayer.com Inc. All rights reserved.

towards understanding by critical constructive inquiry Skicka en kommentar BLOG_CMT_createIframe('https://www.blogger.com/rpc_relay.html'); For when propositions are denied, there is an endof them, but if they bee allowed, it requireth anew worke. The Essais of Sr. Francis Bacon, London, 1612The further a society drifts from the truth, the more it will hate those who speak it. George OrwellNothing is created by coincidence, rather there is reason and necessity for everything. Leukippus, 5th Century BC.De Omnibus Dubitandum