Constant of Proportionality 7 th Grade Chapter 2

Constant of Proportionality 7 th Grade Chapter 2

Standard CC. 7. RP. 2 b Identify the constant of proportionality in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

Essential Question How do I identify the constant of proportionality in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships?

Remember: Unit Rate is… A ratio that has a denominator of one… showing the value of one unit. Examples: price per pound pages read in one hour cups that can fit on one shelf price per gallon

Real World Application If a person walks 4 mile in 2 hours, what is the unit rate? (miles per hour)

Record your information in a table. X independent The independent variable does not depend on anything. Books Y dependent Price 1 5 2 10 3 15 4 20 5 25 6 30 The dependent variable depends on the independent variable in order to find its value.

A straight line through the origin shows a direct proportion on a graph… As x is increasing, y is also increasing. Price dependent Graph It! 10 9 8 7 6 5 4 3 2 1 12 3 4 5 Books independent

Proportionality The graph of a proportional relationship is a straight line that passes through the origin. Proportional quantities can be described by the equation y = kx, where k is a constant ratio. . . also known as constant of proportionality.

Using the form y = kx, write an equation for the information in the chart. X independent What did you multiply x to get y? 5 x = y Books Y dependent Price 1 5 2 10 3 15 4 20 5 25 6 30

If y = kx then doesn’t k = y/x? 5 x = y X independent Books Y dependent Price 1 5 2 10 3 15 4 20 5 25 6 30 The constant of proportionality is 5. To find the constant of proportionality, you can divide the y coordinate by the x coordinate. 5/1 = 5 10/2=5 15/3=5 20/4=5 25/5=5 30/6=5

Constant of Proportionality Do you remember where the 5 came from? The unit rate…it is the number that you used to multiply by each x value to get each y value. Unit rate is also known as the constant of proportionality because it is the number that remains constant in each proportional situation.

Write the unit rate: Read 80 pages in 2 hours 40 _______ pages in one hour

Record your information in the table. Which is the dependent variable? Which is the independent variable? X independent Y dependent Hours Pages 1 40 2 80 3 120 Is this a direct proportion? Yes…as x increases by the What is the same rate, constant of by proportionality? y increases by the same rate.

How do you determine if the graph is a direct proportion? dependent Pages Graph It! 100 90 80 70 60 50 40 30 20 10 12 3 4 5 A straight line through the origin shows a direct proportion. independent Hours

Write the unit rate: A plane travels 2250 km in 3 hours. What is the average speed? (km per hour) They are asking for unit rate… 750 km/hr What is the constant of proportionality? 750

Is this a direct proportion? Yes…A straight line through the origin shows a direct proportion. dependent Km Graph It! 2500 2250 2000 1750 1500 1250 1000 750 500 250 12 3 4 5 independent Hours

y x Find the first point on the graph and name it using the form (x, y). (2, 20) Plug those into the formula to find the constant of proportionality. k = y/x k = 20/2 k = 10

k = 2 Write the equation for the graph above. y = 2 x

X y 1 10 2 20 3 30 4 40 5 50 Write an equation for the information in the table. y = 10 x What is the constant of proportionality? 10

k = 5 Write the equation for the graph above. y = 5 x

k = 7. 5 Write the equation for the graph above. y = 7. 5 x

Y = 12/x No. The equation is not in the form y = kx.

k = 12. 5

Closing How do you find the constant of proportionality from a: Ratio? Table? Equation? Graph? How do you determine if the proportional relationship shown is a direct proportion in a: Table? Graph?