Proportional Equations and Graphs

Proportional Equations and Graphs

Learning Targets:

Nov. 4/5: I can prepare to show mastery on unit rates and proportional tables.

Nov . 9/10: I can review the properties of proportional graphs and equations.

Nov. 11/12: I can review proportional graphs, equations, and tables to reach mastery on an assessment.

Question #1: Review Unit Rates

• a comparison where the second quantity is ONE

• When expressed as a fraction this is the denominator

• EXAMPLE: laps per hour

• Per means division

• EXAMPLE: Ciara ran 12 blocks in 4 minutes. If she ran at a constant speed, how long did it take her to run 1 block?

• Find blocks per minute

• 
  

   $12\ \div4$  

Multiple Choice

Kyle ran 20 blocks in 5 minutes. If she ran at a constant speed, how long did it take him to run 1 block?

• 6 blocks per minute

• 4 blocks per minute

• 5 blocks per minute

• 1 block per minute

Question #2: Fractions and Unit Rates!

• Review Desmos Scientific Calculator

• https://www.desmos.com/scientific

• EXAMPLE: 2. It took Makayla 1/2 of an hour to ride her bike  $2\ \frac{1}{2}$  miles. How many miles per hour did Makayla ride?

Multiple Choice

It took Anna 1/4 of an hour to ride her bike 

 $1\ \frac{1}{2\ }$  miles. How many miles per hour did she travel?

• 4 miles per hour

• 3 miles per hour 

• 2 miles per hour 

• 6 miles per hour 

Question #3: Find the constant from a table

• constant = k

•  $\frac{y}{x}or\ y\div x$  

• EXAMPLE: Find the constant rate between time and water used?

Multiple Choice

What is the constant of proportionality?

• 15
• 5
• 75
• 25

Question #4: How to identify proportional tables.

• Find X and Y.

• Find the constant = y /x

• If all ratios have the same constant the table is PROPORTIONAL!

• Is this table proportional?

Multiple Choice

Determine if the table above is proportional and how do you know?

• The table is proportional because the unit rate is a constant 0.33.
• The table is proportional because it passes through the origin.
• The table is proportional because the unit rate is a constant 0.28
• The table is not proportional because the unit rate is not constant.

Question #5: Find the missing value in a table!

• Find the constant =

   $y\ \div\ x$  

• Use the constant to find the missing information

• 
  

• 
  

Multiple Choice

Find the value of x

• x = 3

• x = 30

• x = 1/3

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All Proportional Graphs ...

• have points that create a straight line

• go through the origin (0,0)

Proportional Graphs

Is this graph proportional?

Why or why not?

Multiple Choice

Does this graph represent a proportional relationship?

• Yes
• No

Multiple Choice

Does this graph represent a proportional relationship?

• Yes
• No

How to find the constant from a graph!

• Remember constants are like unit rates

• Unit rates: a relationship where the second quantity is ONE

• Look at the x axis (left to right), and find 1

• Then go down to the left of the graph or y axis!

• This number is your constant!

Multiple Choice

What is the constant?

• 10

• 5

• 1

• 2

Multiple Choice

What is the constant for the rain fall?

• 2 cm per hour

• 1 cm per hour

• ¹/₂ cm per hour

• 4 cm per hour

All Proportional Equations ...

• use the form y = kx

• k is the constant

• EXAMPLES:

• y = 3x

• y= 1/2x

• y = 5/3x

• y=12x

Multiple Choice

Does this equation represent a proportional relationship?

• Yes

• No

Multiple Choice

Does this equation represent a proportional relationship?

• Yes

• No

Write an equation from a table!

•  $Find\ y\ \div x$  = constant 
  

• Remember the form for equations y = kx

• Replace the letter k with your constant 

• Example: y = 9x

Multiple Choice

Write an equation for this relationship.

• y=1/5x
• y=1/2x
• y=2x
• y=5x

Multiple Choice

Write the equation for the table given

• y = 1/3x
• y = 3x
• y = 1/2x
• x = 3y