Finding the Constant of Proportionality

Miss Jacobson explains how to find the constant of proportionality in proportional graphs. She uses examples of water usage and hiking distance graphs to illustrate the concept. By setting up tables and analyzing the data points, she demonstrates how to calculate the constant of proportionality, which is the number that multiplies the x-value to yield the y-value. She also provides tips for handling cases where the constant is not immediately obvious, such as using a y/x column to simplify calculations.

What is the constant of proportionality in a proportional graph?

• The ratio of y to x

• The sum of x and y variables

• The number you multiply x by to get y

• The difference between x and y variables

In the water usage example, what is the constant of proportionality?

• 7

• 5

• 10

• 3

How can you find the constant of proportionality using a table?

• By adding x and y values

• By subtracting x from y

• By multiplying x by a constant to get y

• By dividing y by x

In the hiking distance example, what is the constant of proportionality?

• 5/6

• 6/5

• 7/5

• 8/5

Why is it sometimes difficult to find the constant of proportionality directly?

• Because x and y are always equal

• Because the constant can be a rational number

• Because the constant is always a whole number

• Because x and y are unrelated

What is the purpose of adding a y over x column in the table?

• To determine the constant of proportionality

• To find the sum of x and y

• To calculate the difference between x and y

• To check if x and y are proportional

How do you calculate the constant of proportionality using the y over x column?

• By finding the average of y over x values

• By adding all y over x values

• By reducing the y over x ratio to its simplest form

• By multiplying all y over x values

What is the result of reducing the ratio 18/15 in the hiking example?

• 8/5

• 5/6

• 6/5

• 7/5

Why is the 0,0 point not useful in finding the constant of proportionality?

• Because it results in division by zero

• Because it is not a valid data point

• Because it is always zero

• Because it does not affect the constant

What should you do if the constant of proportionality is not clear from the table?

• Ignore the data

• Use a different method

• Guess the constant

• Create a y over x column