Constant of Proportionality of Graphs TeacherTwins©2014

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=1/2x, proportional, Constant of prop. 1/2 Y= x + 6, not prop. Y = 2x, proportional, Constant of prop. 2

The black line is proportional. The blue line is not proportional. 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. How are these lines alike? Different? Proportional graphs are straight and go through the origin.

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 you did not buy any gummies so you did not spend any money. It means one pound cost $2.00.

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? Write the equation. Graph the equation. Pounds Price 2 3 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? Write the equation. Y= 1.50x Graph the equation. Pounds Price 2 $3.00 3 $4.50 4 $6.00 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

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

How do you know if a graph is proportional? Closure How do you know if a graph is proportional?