Proportional vs. Non-proportional Thursday, April 27, 2017

Review Key Vocabulary Proportional – when two quantities that simplify to the same ratio. Constant – a quantity having a value that does not change or vary. Constant of Proportionality - a constant value of the ratio of two proportional quantities.

Proportionality Two quantities are directly proportional if they have a constant ratio . The change in one variable is always accompanied by a change in the other. This constant ratio is called the “constant of proportionality”. The constant of proportionality can never be zero.

Proportional Relationships Identify the constant of proportionality: The constant of proportionality is the unit rate From the table, look at the ratio of y to x From the graph, look at the steepness of the graph or look for the y-value where x is one From the equation, look for the coefficient of x

Proportional vs. Non-Proportional Two quantities are directly proportional if they have a constant ratio . If the ratio is not constant, the two quantities are non-proportional. We will look at tables, graphs, equations, and ordered pairs to determine if the relationship between the variables is proportional.

Equations: You should also be able to write equations to describe the relationships. If the situation is proportional, you will use your constant of proportionality in your equation. Be sure to define your variables!!!

Proportional relationships: tables In order to tell from a table if there is a proportional relationship between the variables, you should check to see if the ratio is the same for all values in the table. The ratio is also known as the scale factor. Reduce or divide to find the constant of proportionality (unit rate) that defines the relationship between the variables.

Determine if the tables below represent a proportional relationship. Pounds (x) Cost (y) 4 $1 6 $1.50 8 $2 10 $2.50 Number of books (x) Price (y) 1 3 9 4 12 7 18 Proportional? ________ Ratio __________ Equation ___________ Const of Prop __________ Proportional? ________ Ratio __________ Equation ___________ Const of Prop __________

Proportional? ________ Ratio __________ Equation ___________ Const of Prop __________

Proportional? ________ Ratio __________ Equation ___________ Const of Prop __________

Proportional? ________ Ratio __________ Equation ___________ Const of Prop __________

Proportional Relationships: graphs The graph of a proportion will always be a straight line that passes through the origin (0,0). Always write the constant ratio in the form of .

LearnZillion Notes: --For some lessons it may be best to include a slide or two about “A Common Mistake.” These slides show students what mistakes to avoid so that they can follow the Core Lessons more easily. --Feel free to move or resize the blue text box to fit your content. --Remember that you can add multiple “A Common Mistake” slides if you need them or you can just delete this slide!

Determine if the graphs below represent a proportional relationship. Why? Line goes thru the origin Why? Line does not go thru the origin

How does the average speed from hour 1 to hour 4 compare to the average speed from hour 5 to hour 6? One way to estimate between which pair of coordinates the average speed was greater is to look at the graph and see where the rate of change, or change in miles per change in hours was greater, which would subsequently make the line graph steeper. The line segment between hour 5 and 6 appears to be steeper to me than the line segment between hour 1 and 4, but to make sure, let’s find the precise average speed between each pair of coordinates.

How does the average speed from hour 1 to hour 4 compare to the average speed from hour 5 to hour 6? One way to estimate between which pair of coordinates the average speed was greater is to look at the graph and see where the rate of change, or change in miles per change in hours was greater, which would subsequently make the line graph steeper. The line segment between hour 5 and 6 appears to be steeper to me than the line segment between hour 1 and 4, but to make sure, let’s find the precise average speed between each pair of coordinates.

Proportional? How can You determine the unit rate from a graph? Constant of proportionality? Equation?

Proportional? How can You determine the unit rate from a graph? Constant of proportionality? Equation?

Proportional? How can You determine the unit rate from a graph? Constant of proportionality? Equation?

Proportional relationships: equations Determine if the following equations show a proportional relationship. Substitute a zero for x in the equation and then solve. If y then equals zero, then the equation represents a proportional relationship because the graph of the line goes through the origin. y = 3x – 1 y = 10x