Proportionality of Tables and Equations Teacher Twins 2014

Warm Up Find four solutions to each equation and graph them. Choose your own values for x. 1). Y = -2 x 2). Y = x + 1 3). Y = 3 x - 1

Warm Up 1). Y = -2 x (blue) 2). Y = x + 1 (red) 3). Y = 3 x – 1 (yellow)

Review What is a ratio? Give an example. What is a proportion? Give an example.

Determine if the Table is Proportional Example 1: X -2 -1 0 1 2 Y -4 -2 0 2 4 A table is proportional if the ratios of y to x are all equal. We can’t make a ratio when x is zero, so we will skip it. This table is proportional.

Determine the Constant of Proportionality Example 1: X -2 -1 0 1 2 Y -4 -2 0 2 4 The constant of proportionality is the constant value of the ratio of two proportional quantities y and x.

Determine if the Equation is Proportional Example 1: X -2 -1 0 1 2 Y -4 -2 0 2 4 Equations that are proportional are written y = kx, where k is the constant of proportionality. The equation for this table is Y = 2 x. The constant of proportionality is 2.

Example 2: Tell if the table is proportional. If it is proportional, give the constant of proportionality. X -2 -1 0 1 2 Y -2 0 2 4 6 This table is not proportional because the ratios are not equal. There is no constant of proportionality.

Example 2: What is the equation for this table? X -2 -1 0 1 2 Y -2 0 2 4 6 y = 2 x + 2 This table is not proportional so the equation is not proportional. Proportional equations are written y=kx. There is no constant of proportionality.

Example 3: Jackie wants to buy some pencils for school. If each pencil cost 15 cents, how much will she pay for 3, 5, and 10 pencils? Fill in the table for the problem. Pencil 3 Price $0. 45 5 $0. 75 10 $1. 50 What is the equation? Y=0. 15 x Is this proportional? If it is give the constant of proportionality. Proportional, COP=0. 15

Practice Determine if the equations are proportional. Y = 2 x Y= -3 x Y= 1/2 x Y=2 x-4 Y=x+3 Y=2 x+12 Y= -12+x Y= x-4

Practice Write the equation for each table. Determine if the table is proportional and give the constant of proportionality. Y= 3 x+1, not prop. Y = x + 9, not prop. Y = 3 x, proportional, constant of prop. Is 3.

Practice 4). Allie can run 3 miles in one hour. How many miles can she run in 2, 4 and 6 hours? Hours Miles 2 4 6 6 12 18 What is the equation? Y = 3 x Tell if the table is proportional and give the constant of proportionality. It is proportional, the COP is 3

Closure What do the equations of proportional tables look like? What do the equations of nonproportional tables look like?