Constant of Proportionality of Graphs Teacher Twins 2014

Warm Up Tell if the table is proportional. Explain why or why not. Give

The black line is proportional. The blue line is not proportional. How are these

No, it does not go through the origin It does not have one because

Yes, it is straight and goes through the origin. The constant of proportionality is

It means one pound cost $2. 00. It means you did not buy any

Example 4: Kim bought one pound of grapes for $1. 50. How much will

Practice Tell if the graph is proportional and give the constant of proportionality. 1).

3). Stephen can ride 12 miles in one hour on his bike. How many

Closure How do you know if a graph is proportional?

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Warm Up Tell if the table is proportional. Explain why or why not. Give the constant of proportionality and give the equation for each table. Y=1/2 x, proportional, Constant of prop. 1/2 Y= x + 6, not prop. Y = 2 x, proportional, Constant of prop. 2

The black line is proportional. The blue line is not proportional. How are these lines alike? Different? Proportional graphs are straight and go through the origin. The constant of proportionality is the y value when x is one. The constant of proportionality for the black graph is 1. The blue graph does not have one because it is not proportional.

No, it does not go through the origin It does not have one because it is not proportional.

Yes, it is straight and goes through the origin. The constant of proportionality is -1.

It means one pound cost $2. 00. It means you did not buy any gummies so you did not spend any money.

Example 4: Kim bought one pound of grapes for $1. 50. How much will she pay for 2, 3, and 4 pounds of grapes? Pounds 2 3 Price Write the equation. Graph the equation. 4 Tell if it is proportional and give the constant of proportionality.

Example 4: Kim bought one pound of grapes for $1. 50. How much will she pay for 2, 3, and 4 pounds of grapes? Pounds Price 2 $3. 00 3 $4. 50 4 $6. 00 Write the equation. Y= 1. 50 x Graph the equation. Tell if it is proportional and give the constant of proportionality. Yes, it is proportional. The COP is 1. 50.

Practice Tell if the graph is proportional and give the constant of proportionality. 1). Not proportional, no COP 2). Proportional, COP=2

3). Stephen can ride 12 miles in one hour on his bike. How many miles will he ride in 3, 5, and 6 hours? Pounds 3 5 Price Write the equation. Graph the equation. 6 Tell if it is proportional and give the constant of proportionality. 80 70 60 50 40 30 20 10 1 2 3 4 5 6 7 8 9

3). Stephen can ride 12 miles in one hour on his bike. How many miles will he ride in 3, 5, and 6 hours? Pounds Price 3 36 5 60 6 72 Write the equation. Y= 12 x Graph the equation. 80 Tell if it is proportional and give the 70 constant of proportionality. 60 50 It is proportional, 40 the COP is 12. 30 20 10 1 2 3 4 5 6 7 8 9

Closure How do you know if a graph is proportional?