5 Minute Check Complete in your notes. MegaMart collects a sakes tax equal to 1/16 of the retail price of each purchase. The tax is sent to the government.

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Proportional Relationships

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Presentation transcript:

5 Minute Check Complete in your notes. MegaMart collects a sakes tax equal to 1/16 of the retail price of each purchase. The tax is sent to the government. 1. Is the amount of tax collected proportional to the cost of an item before the tax is collected? Explain. 2. Is the amount of tax collected proportional to the cost of an item after tax has been added? Explain.

5 Minute Check Complete in your notes. MegaMart collects a sakes tax equal to 1/16 of the retail price of each purchase. The tax is sent to the government. 1. Is the amount of tax collected proportional to the cost of an item before the tax is collected? Explain.

5 Minute Check Complete in your notes. MegaMart collects a sakes tax equal to 1/16 of the retail price of each purchase. The tax is sent to the government. 1. Is the amount of tax collected proportional to the cost of an item before the tax is collected? Explain.

5 Minute Check Complete in your notes. MegaMart collects a sakes tax equal to 1/16 of the retail price of each purchase. The tax is sent to the government. 2. Is the amount of tax collected proportional to the cost of an item after tax has been added? Explain.

5 Minute Check Complete in your notes. MegaMart collects a sakes tax equal to 1/16 of the retail price of each purchase. The tax is sent to the government. 2. Is the amount of tax collected proportional to the cost of an item after tax has been added? Explain.

Monday, Jan 12 Lesson Graph Proportional Relationships

Objective: To identify proportional relationships by graphing on the coordinate plane. You will need your graph paper for today’s lesson.

Graph Proportional Relationships Another way to determine whether two quantities are proportional is to graph the quantities on the coordinate plane. If the graph of the two quantities is a straight line through the origin, then the two quantities are proportional.

Graph Proportional Relationships The slowest animal on Earth is the three sloth. It moves at a speed of 6 feet per minute. Determine whether the number of feet the sloth moves is proportional to the number of minutes it moves by graphing on the coordinate plane. Explain your reasoning. Determining Proportions by Graphing Step 1 – Make a table.

Graph Proportional Relationships The slowest animal on Earth is the three sloth. It moves at a speed of 6 feet per minute. Determine whether the number of feet the sloth moves is proportional to the number of minutes it moves by graphing on the coordinate plane. Explain your reasoning. Determining Proportions by Graphing Step 1 – Make a table.

Graph Proportional Relationships The slowest animal on Earth is the three sloth. It moves at a speed of 6 feet per minute. Determine whether the number of feet the sloth moves is proportional to the number of minutes it moves by graphing on the coordinate plane. Explain your reasoning. Determining Proportions by Graphing Step 2 – Graph the coordinates.

Graph Proportional Relationships The slowest animal on Earth is the three sloth. It moves at a speed of 6 feet per minute. Determine whether the number of feet the sloth moves is proportional to the number of minutes it moves by graphing on the coordinate plane. Explain your reasoning. Determining Proportions by Graphing Step 2 – Graph the coordinates.

Graph Proportional Relationships The slowest animal on Earth is the three sloth. It moves at a speed of 6 feet per minute. Determine whether the number of feet the sloth moves is proportional to the number of minutes it moves by graphing on the coordinate plane. Explain your reasoning. If the graph is a straight line and passes through the origin, it is Proportional. Is this graph proportional?

Graph Proportional Relationships James earns $5 an hour babysitting. Determine whether the amount of money he earns is proportional to the number of hours he babysits by graphing by on the coordinate plane. Explain your reasoning. Do this on your own.

Graph Proportional Relationships James earns $5 an hour babysitting. Determine whether the amount of money he earns is proportional to the number of hours he babysits by graphing by on the coordinate plane. Explain your reasoning. Since the graph is a straight line and passes through the origin, the time-to- money is proportional.

Graph Proportional Relationships Determine whether the number of pizzas is proportional to the amount of cheese by graphing by on the coordinate plane. Explain your reasoning. Do this on your own.

Graph Proportional Relationships Determine whether the number of pizzas is proportional to the amount of cheese by graphing by on the coordinate plane. Explain your reasoning. (sometimes you may need to extend the line to see if it passes through the origin) Since the graph is a straight line and passes through the origin, the pizzas-to- cheese is proportional.

Graph Proportional Relationships The cost of renting a video game from Games, Inc is shown in the table. Determine whether the cost is proportional to the numbers of games rented by graphing by on the coordinate plane. Explain your reasoning. Do this on your own.

Graph Proportional Relationships The cost of renting a video game from Games, Inc is shown in the table. Determine whether the cost is proportional to the numbers of games rented by graphing by on the coordinate plane. Explain your reasoning. Since the graph is a straight line but does not pass through the origin, the cost-to- game is nonproportional.

Graph Proportional Relationships Which batting cage represents a proportional relationship between the number of pitches thrown and the cost? Explain your reasoning.

Graph Proportional Relationships Which batting cage represents a proportional relationship between the number of pitches thrown and the cost? Explain your reasoning. Softball Plus is a straight line, but does not pass through the origin. It is nonproportional. Fun Center is a straight line, but does pass through the origin. It is proportional.

Graph Proportional Relationships A proportion is an equation stating two rates or ratios are equivalent.

Graph Proportional Relationships A proportion is an equation stating two rates or ratios are equivalent. Two rates or ratios are equivalent if their cross products are equal.

Graph Proportional Relationships Two rates or ratios are equivalent if their cross products are equal. 6 · 4 = 24

Graph Proportional Relationships Two rates or ratios are equivalent if their cross products are equal. 6 · 4 = 24 8 · 3 = 24 Since the cross products are equal, they are equivalent.

Graph Proportional Relationships Is this a true statement?

Graph Proportional Relationships Is this a true statement? · 2 = · 3 = 12 It is not a true statement

Graph Proportional Relationships Is this a true statement?

Graph Proportional Relationships Is this a true statement? · 10 = · 13 = 101 It is not a true statement

Graph Proportional Relationships Is this a true statement?

Graph Proportional Relationships Is this a true statement? · 40 = · 50 = 600 It is a true statement

Graph Proportional Relationships Is this a true statement?

Graph Proportional Relationships Is this a true statement? · 12 = · 17 = 272 It is not a true statement

Graph Proportional Relationships Johanna’s parents give her $10 per week for lunch money. The greenhouse temperatures at certain times are shown in the table. The greenhouse maintains temperatures between 65°F and 85°F. Suppose the temperature increases as a constant rate. Create a graph of the time and temperatures at each hour from 1PM and 8PM. Is the relationship proportional? Explain.

Graph Proportional Relationships Johanna’s parents give her $10 per week for lunch money. The greenhouse temperatures at certain times are shown in the table. The greenhouse maintains temperatures between 65°F and 85°F. Suppose the temperature increases as a constant rate. Create a graph of the time and temperatures at each hour from 1PM and 8PM. Is the relationship proportional? Explain. Since the straight line does not pass through the origin, it is not proportional.

Proportional and Nonproportional Relationships Agenda Notes Homework – Homework Practice Due Tuesday, Jan 13 Mid-Chapter Quiz – Tuesday, Jan 13 Chapter 7.1 Test - Friday, Jan 16