# What is a Proportionality?

## Answers

1) You can divided all of the distances by the time. The result will be 3/4 in each case, therefore it is proportional.

2) For the equation, you can multiply the time by 3/4 and it will equal the distance. You can put the values you have into a table and graph them to also show it is proportional.

3) Since there is a constant factor between the two values, they are proportional.

60 rev/min (Answer D)

Step-by-step explanation:

Calculate it!

2400 revolutions

= 60 rev/min

40 minutes

Step-by-step explanation:

A) The constant of proportionality in terms of minutes per bracelet is

15/3 = 5 minutes per bracelet

B) The constant of proportionality represents man hour rate

C) let k = constant of proportionality, t = time in minutes and b = number of bracelets produced. Therefore,

t = kb

D) the constant of proportionality in terms of number of bracelets per minute is

3/15 = 1/5

E) The constant of proportionality represents production rate

F) let k = constant of proportionality, t = time in minutes and b = number of bracelets produced. Therefore,

b = kt

G) The constants of proportionality are reciprocals

H) Two equations are equivalent if they have the same solution. They are not equivalent. By inputting the different values of k, the solutions will always be the same. Therefore, they are equivalent.

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In graphs of linear relationships, you can always determine a proportional linear relationship by observing where the line crosses the y axis. If the line crosses through the origin, then the relationship is proportional. This means that the independent data(in this case time) can be multiplied by a constant factor to always get it's related dependent piece of data.

From the graph you might notice some data points for Gary: At 2mins he completes 1.5 knots or the ordered pair (2, 1.5). We see another data point at 4mins he completes 3 knots or the ordered pair (4,3). How about the ordered pair (6, 4.5)? Notice that if I multiply the "x" coordinate of all these ordered pairs by 0.75, I get the "y" coordinate. Or maybe another way to look at it, the "y" coordinate of each point on the line divided its corresponding "x" coordinate will always produce the same number, 0.75. This number, 0.75, is called the constant of proportionality.

So, the answer to this problem is choice "D"

Summary: To identify proportional linear relationship from a graph, look for the line that goes through the origin. To find the constant of proportionality, determine the coordinates of a convenient point on the line and divide the y coordinate by the x .

Option A is the correct answer.

Explanation:

There are 6 packages that store 30 baseball cards.

Number of cards in 1 package = 30/6 = 5

Let us consider a as number of packages and b as number of cards.

We have equation for number of cards,

b = 5 a

The constant of proportionality = 5

Option A is the correct answer.

The first one, 5×10 is 50 making each one cost 5

Yes, the are proportional. To do this, just divide the distance in each example by the number of minutes. You will get 3/4 each time, so they are proportional.

For your table, just create 3 columns.

Distance Time Rate

2/3 1/4 3/4

If you make a table, you will have the same rates. If you graph the data, it will be linear through the origin. Both ways prove that it is proportional.

The quality of corresponding in size or amount to something else.