Representing Proportional Relationships with Equations.

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Presentation transcript:

Representing Proportional Relationships with Equations

a.Find the constant of proportionality and explain what it represents in this situation. b.Write equation(s) that will relate the miles driven to the number of gallons of gas (y = __x) c.Knowing that there is a half a gallon left in the gas tank when the light comes on, will she make it to the nearest gas station? Explain why or why not. d. Using the equation from b, determine how far mom can travel on 18 gallons of gas e. Using the equation from b, determine how many gallons of gas would be needed to travel 750 miles

The Equation on a Graph If we were graphing this situation, what would be the dependent and what would be the independent variable? Independent Dependent Gallons of gas Miles Driven

Lets write the data from the table as ordered pairs. Which points will represent our independent variable (x), and which points will represent our dependent variable (y)?

(1, 28) (8, 224) 10, 280) (4, 112)

c. What is the unit rate and what is the constant of proportionality?

Day 2 Lets use b = # of birdhouses and h = # of hours

Does it matter which of these is the independent or dependent variable? If we want to determine the number of birdhouses that can be built in one hour, what is the constant of proportionality? What does it mean in the context of this situation? If we want to know how many hours it takes to build one birdhouse, what is the constant of proportionality? What does it mean in the context of this situation?

How many birdhouses can Jackson build in 40 hours? How long will it take Jackson to build 35 birdhouses? (Give your answer in hours and minutes) How long will it take to build 71 birdhouses? (Give your answer in hours and minutes)

Find each unit rate Al’s unit rate __________ Barbara’s unit rate ___________ Determine which variable is dependent and which variable is independent Equation for Al’s Produce Stand y = _____x Equation for Barbara’s Produce Stand y = _____x Write each equation using the variable E = ears of corn and C = cost of corn

Closing In order to write a proportional relationship in the form y = kx, what do you need to know? Give me a real life example that can be modeled using this type of equation How do you determine which is the independent and which is the dependent variable? Give a real world example that could NOT be modeled by this type of equation