Identify proportional or nonproportional
Solving Proportions
Constant Rate of Change
Proportional
Vocabulary
100
Which situation represents a proportional relationship between the number of laps run by each student and their time?
What is the table for Desmond’s Time shows a proportional relationship?
(The ratio between the time and the number of laps is always 73.)
100
Solve the proportion.
What is p= 20?
100
Find the constant of proportionality for the table.
What is $9 per item?
100
Determine whether the linear relationship is a direct variation. If so, state the constant of proportionality.
What is yes, k =8?
100
(0,0) represents the _______________.
What is origin?
200
Determine whether the relationship between the two quantities shown in each table are proportional by graphing on the coordinate plane. Explain your reasoning.
What is proportional? The graph is a straight line through the origin.
200
Solve the proportion.
What is d= 7.2?
200
The graph shows the cost of purchasing T-shirts.
Find the constant rage of change for the graph.
The cost increases by $9 per shirt.
200
Determine whether the linear relationship is a direct variation. If so, state the constant of proportionality.
What is no?
200
A rate that has a denominator of 1 unit is called a _______________ rate.
What is a unit?
300
Determine whether the relationship between the two quantities shown in each table are proportional by graphing on the coordinate plane. Explain your reasoning.
What is Not proportional?
The graph does not pass through the origin.
300
Assume the situation is proportional. Write and solve by using a proportion.
Sheila mixed 3 ounces of blue paint with 2 ounces of yellow paint. She decided to create 20 ounces of the same mixture. How many ounces of yellow paint does Sheila need for the new mixture?
What is 8 ounces?
300
Find the constant rate of change for the table.
What is 6 meters per second?
300
The money Shelley earns varies directly with the number of dogs she walks. How much does Shelley earn for each dog she walks?
What is $2 per dog?
300
A _______________ is an equation stating that two ratios or rates are equal.
What is a proportion.
400
FIND THE ERROR Blake ran laps around the gym. His times are shown in the table. Blake is trying to decide whether the number of laps is proportional to the time. Find his mistake and correct it.
What is it is not proportional because the ratio of laps to time is not consistent; .
400
Assume the situation is proportional. Write and solve by using a proportion.
Evarado paid $1.12 for a dozen eggs at his local grocery store. Determine the cost of 3 eggs.
What is 28 cents?
; $0.28
400
The cost of 1 movie ticket is $7.50. The cost of 2 movie tickets is $15. Based on this constant rate of change, what is the cost of 4 movie tickets?
What is $30?
400
Determine if each equation represents a direct variation. Select yes or no.
a.
b.
c.
d.
What is no, yes, yes, no?
400
Two Vocab Words.
The multiplier in a proportional equation represented by K. It is also the __________ ______________.
Constant of Proportionality, unit rate
500
The height of two plants is recorded after 1, 2, and 3 weeks as shown in the graph at the right. Which plants’ growth represents a proportional relationship between time and height? Explain.
What is plant B?
(The graph is a straight line through the origin.)
500
Assume the situation is proportional. Write and solve by using a proportion.
For every person who actually has the flu, there are 6 people who have only flu-like symptoms. If a doctor sees 40 patients, determine approximately how many of these you would expect to have only flu-like symptoms.
What is 34 patients?
; about 34 patients
500
Use the graph to find the constant of proportionality. Then, explain what the points (0, 0) and
(6, 72) represent.
What is 12 pages printed per minute?
The point (0, 0) represents zero pages printed in zero minutes. The point (6, 72) represents 72 pages printed in 6 minutes.
500
Reason Abstractly If y varies directly with x, write an equation for the direct variation. Then find the value.
If y = 14 when x = 8, find y when x = 12.
What is ; 21
500
The rise over run. Represents the rate of change in a proportional graph.
Slope