U9 Prop Relationships 2

​Unit 9
Proportional Relationships
Take 2

By Latter UP Tools

​Review

​

Draw

Which relationships have the same constant of proportionality between y and x as the following table?

X y

2 7

7 24.5

9 31.5

​A connection in which the ratio of one item to the other does not change is known as a proportionate relationship. Stated differently, a constant rate of change in one variable results in a corresponding change in the other. The term "constant of proportionality" is frequently used to describe this consistent rate of change.

​https://www.98thpercentile.com/blog/what-is-proportional-relationship

​1. Financial Planning: Budgeting and finance both frequently employ proportionate connections. You can predict how costs will alter when your family size changes, for instance if your monthly grocery bills are based on the number of family members.

2. Physics and Engineering: Both physics and engineering depend on proportional connections. Phenomena such as density, force, and speed in physics frequently imply proportionality. For instance, Ohm's Law states that the voltage across a conductor is proportional to the current passing through it, as expressed by the formula V=IR, where R is the proportionality constant.

A vast array of issues may be effectively understood and resolved with the use of proportional relationships. We can solve practical issues, make wiser judgments, and handle day-to-day circumstances with ease if we understand the notion of proportionality. Knowing how proportional connections function may help you become more analytical and proficient at solving problems, whether you're evaluating data, budgeting, or modifying recipes.

​Real-World Applications of Proportional Relationships

​Identifying Proportional Relationships:

To find proportional connections, two variables must have constant ratios between them. One can ascertain the proportionality of a connection in several ways:

​Foxes	​Rabbits
​2	​40
​5	​100
​9	​180
​16	​320

​​1. Using Ratios: You may compute the ratio between the respective values of the variables to ascertain whether two variables are proportionate. The connection is proportional if the ratio stays the same for every pair of variables.

Example:
A scientist has been observing the number of foxes to rabbits across a variety regions to determine how many rabbits are needed to support a community of foxes. Using the chart below, determine if this relationship is proportional.

Multiple Choice

Which statement best describes the relationship between x and y in the table?

• Proportional
• Not Proportional

​X	​Y
​1	​1
2​	4​
3​	9
4​	​16

​X	​Y
​2	​1 1/3
​4	​2 2/3
​7	​4 2/3
​10	​6 2/3

Which chart show a proportional relationship?


If it's the red chart touch your nose.

If it's the blue chart touch your chin.

If it's the yellow chart stand on your head.

Multiple Choice

Ruby must fold 2 loads of laundry a week. For every load of laundry Ruby folds after the first two loads she earns $5. Does this represent a proportional relationship?

• YES

• NO

​2. Graphing: Graphic identification of proportional connections is also possible. A proportionate connection between x and y will always result in a straight line passing through the origin (0, 0) when graphed. The slope of this line is equal to the proportionality constant, k.

Multiple Choice

What makes a graph proportional?

• Linear
• The line is only in quadrant 1
• Curvy line
• Straight line and the line goes through the origin

Multiple Choice

Is this graph proportional?

• Yes
• No

Multiple Choice

Why does this graph show a non-proportional relationship?

• Because it is proportional
• It goes through the origin
• It does not go through the origin
• It is a straight line

Multiple Choice

What does the point (2, 94) represent in this situation?

• Every week, they earn $94.
• After 94 weeks, they save $2.
• After 1 week, they save $47.
• After 2 weeks, they save $94.

Multiple Choice

What does the ordered pair (20, 3000) represent?

• The machine folds 3,000 sheets in 20 minutes.
• The machine folds 20 sheets in 3,000 minutes.
• There are 3,000 sheets in 20 minutes.
• There are 20 sheets in 3,000 minutes.

Multiple Choice

Perry earned $96 shoveling snow from 8 driveways.  At that rate, how much would he have made if he had shoveled only 6 driveways?

• $120
• $12
• $84
• $72

​Solving Proportions

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