Proportional Relationships

What is an eureka moment?

• A sudden realization or discovery of a solution to a problem or a new understanding of something.

• A moment of forgetfulness or memory loss

• A gradual process of problem-solving

• A moment of confusion or uncertainty

Who are considered great minds in history?

• Albert Einstein, Leonardo da Vinci, Isaac Newton, Marie Curie, Nikola Tesla

• Thomas Edison

• Galileo Galilei

• Sigmund Freud

What are some examples of proportional relationships?

• Speed and time, height and weight, age and income

• Distance and time, number of workers and amount of work, cost and quantity

What is the difference between direct and inverse proportional relationships?

• In a direct proportional relationship, the variables have no relationship. In an inverse proportional relationship, one variable has no effect on the other.

• In a direct proportional relationship, the variables increase together. In an inverse proportional relationship, one variable increases while the other decreases.

• In a direct proportional relationship, the variables remain constant. In an inverse proportional relationship, one variable remains constant while the other changes.

• In a direct proportional relationship, the variables decrease together. In an inverse proportional relationship, one variable decreases while the other increases.

How can you determine if two quantities are in a proportional relationship?

• By calculating the average of the two quantities.

• By checking if the ratio of the two quantities remains constant.

• By checking if the two quantities have the same units.

• By comparing the sum of the two quantities.

What is the formula to find the constant of proportionality?

• k = y/x

• k = x/y

• k = x+y

• k = x*y

How can you represent a proportional relationship using a table?

• By creating a table with random values that are not related to the independent and dependent variables

• By creating a graph with the values of the independent variable (x) and the corresponding values of the dependent variable (y)

• By creating a table with the values of the independent variable (x) and the corresponding values of the dependent variable (y)

• By creating a table with the values of the dependent variable (y) and the corresponding values of the independent variable (x)

What is the graph of a proportional relationship?

• A parabola

• A curved line

• A horizontal line

• A straight line passing through the origin (0,0)

How can you solve problems involving proportional relationships?

• Use trial and error to find the correct values.

• Guess the missing values.

• Ignore the constant ratio and solve the problem using other methods.

• Identify the constant ratio and use it to find missing values or compare quantities.

What are some real-life applications of proportional relationships?

• Determining the cost of items based on color, calculating distances based on temperature and time, and calculating sales tax based on the day of the week.

• Calculating sales tax, determining the cost of items based on weight or quantity, and calculating distances based on speed and time.