Module 1 Lesson 9 Proportional Relationships and Equations.notebook

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Representing Proportional Relationships with Equations

12/14/16Module 1, Lesson 9

Homework:Lesson 9 Problem Set Page 40#2, 4, 5, 6

Do Now

Module 1 Exam Thursday 12/22

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Problem Set Solutions (continued) 35

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Problem Set Solutions (continued)35

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a. Find the constant of proportionality and explain what it represents in this situation.

Gallons Miles Drivenyx

8 224

10 280

4 112

The constant of proportionality is _________.

The Car travels ______ miles for every one gallon of gas.

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b. Write the equation that will relate the miles driven to the number of gallons of gas.

Steps to figure out the equation.1. Which unit is the dependent variable?

2. Which unit is the independent variable?

3. Find the k.

Constant of Proportionality = k =

4. Plug in the value of k to y = kx.

­The constant

x is known as the independent variable and y as the dependent variable,.

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c. Knowing that there is a half 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.

Using Arithmetic Using Algebra

d. Using the equation found in part b, determine how far your mother can travel on 18 gallons of gas. Solve the problem in two ways.

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e. Using the equation found in part b, determine how many gallons of gas would be needed to travel 750 miles.

Module 1 Lesson 9 Proportional Relationships and Equations.notebook

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a. Write several ordered pairs from the graph and explain what each coordinate pair means in the context of this graph.

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(0,0) ‐ It takes Andrea 0 hours to draw 0 portraits

(2,3) ‐ It takes Andrea 2 hours to draw 4 portraits

(4,6) ‐ It takes Andrea 4 hours to draw 6 portraits

(6,9) ‐ It takes Andrea 6 hours to draw 9 portraits

Tap

Module 1 Lesson 9 Proportional Relationships and Equations.notebook

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b. Write several equations that would relate the number of portraits drawn to the time spent drawing the portraits.

c. Determine the constant of proportionality and explain what it means in this situation.

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Problem Set 40

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Problem Set 40

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Closing Question

How can unit rate be used to write an equation relating two variables that are proportional? The unit rate is the constant of proportionality, k. After computing the value for k, it may be substituted in place of k in the equation y = kx. The constant of proportionality can be multiplied by the independent variable to find the dependent variable, and the dependent variable can be divided by the constant of proportionality to find the dependent variables.

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