The graph below is one of a proportional relationship. Enter a value for x or y and press the Enter key of your keyboard. The corresponding value is immediately given by the curve. Try other values and establish a relation between the x and y coordinate. What is the constant of proportionailty?

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**Plot Graphs of Linear Relations from Tables.**

**(A). The equation could represent a variety of different situations.**

(1). Write a description of a situation represented by this equation. Decide what quantities and represent in your situation.

(2). Make a table to represent the situation.

(3). Graph this situation using your table. Remember to number and label your axes.

(B). Elena babysits her neighbor’s children. Her earnings are given by the equation where represents the number of hours she worked and represents the amount of money she earned. Jada earns $7 per hour mowing her neighbors’ lawns.

(1). Who makes more money after working 12 hours?

(2). How much more do they make?

(3). Explain your reasoning by creating a graph or a table by choosing below.

(4). What is the rate of change for each situation and what does it mean?

(5). Using your graph or table, determine how long it would take each person to earn $150.

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**Compare Graphs of Linear Relationships.**

**(A). Clare and Han have summer jobs stuffing envelopes for two different companies.**

(1). Create a graph of this situation below. Use the graph below to help you answer the questions that follow. Remember to number and label your axis.

(2). What is the rate of change for each situation and what does it mean?

(3). Using your graph, determine how much more money one person makes relative to the other after stuffing 1,500 envelopes. Explain or show your reasoning.

Han and Clare are still stuffing envelopes. Han can stuff 20 envelopes in a minute, and Clare can stuff 10 envelopes in a minute. They start working together on a pile of 1,000 envelopes.

(4). How long does it take them to finish the pile?

(5). Who earns more money?

**(B). Tyler plans to start a lemonade stand and is trying to perfect his recipe for lemonade. He wants to make sure the recipe doesn’t use too much lemonade mix (lemon juice and sugar) but still tastes good.**

(1). If Tyler had 16 cups of lemonade mix, how many cups of water would he need for each recipe? Explain your reasoning by creating a graph or a table.

(2). Make a table to represent the situation.

(3). Graph this situation using your table. Remember to number and label your axes.

(4). What is the rate of change for each situation and what does it mean?

(5). Tyler has a 5-gallon jug (which holds 80 cups) to use for his lemonade stand and 16 cups of lemonade mix. Which lemonade recipe should he use? Explain or show your reasoning.

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**More About Comparing Graphs of Linear Relatiuonships.**

A contractor must haul a large amount of dirt to a work site. She collected information from two hauling companies.

(1). How much would each hauling company charge to haul 40 cubic yards of dirt? Explain or show your reasoning.

(2). Calculate the rate of change for each relationship. What do they mean for each company?

(3). If the contractor has 40 cubic yards of dirt to haul and a budget of $1000, which hauling company should she hire? Explain or show your reasoning.

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Andre and Priya are tracking the number of steps they walk. Andre records that he can walk 6000 steps in 50 minutes. Priya writes the equation , where is the number of steps and is the number of minutes she walks, to describe her step rate. This week, Andre and Priya each walk for a total of 5 hours. Who walks more steps? How many more?

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(1). Find the coordinates of point ** A** in each diagram:

(2). Find the coordinates of point ** B **in each diagram:

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Select **all** the pairs of points so that the line between those points has slope .

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