If you know that a relationship between two quantities is proportional, what information do you need to write an equation that represents the relationship? Support your answer with an example
To write an equation that represents a proportional relationship between two quantities, you need to know the constant of proportionality. The constant of proportionality represents the ratio between the two quantities and allows you to establish a direct relationship between them.
For example, let's say you know that the relationship between the number of hours worked (H) and the amount of money earned (M) is proportional, and the constant of proportionality is $10 per hour. To write an equation representing this relationship, you would use the following formula:
M = 10H
In this equation, the constant of proportionality is 10. This means that for every hour worked, $10 will be earned. As the number of hours worked increases, the amount of money earned will also increase in a proportionate manner.
summarize and dumb it down
When two quantities have a proportional relationship, it means that they increase or decrease together in a consistent way. To write an equation for this relationship, you need to know a special number called the constant of proportionality. This number tells you how much one quantity changes for each unit change in the other quantity.
For example, imagine you earn $10 for every hour you work. If you want to write an equation for this relationship, you can say "the amount of money you earn (M) is equal to $10 times the number of hours you work (H)" or more simply: M = 10H.
This equation shows that as the number of hours you work increases, the amount of money you earn also increases by $10 for each hour worked.
summarize it into 3 sentences and say it like your tellling a kid
When two things are related proportionally, it means they go up or down together in a nice even way. To write it down, you need a special number that tells you how much one thing changes when the other thing changes. For example, if you earn $10 for every hour you work, you can write it like this: M = 10H. This means that for each hour you work, you get $10 more.
To write an equation that represents a proportional relationship between two quantities, you need to know the constant of proportionality. The constant of proportionality represents the ratio between the two quantities.
Let's say we have a proportional relationship between the number of hours worked and the amount of money earned per hour. Let "x" be the number of hours worked, and "y" be the amount of money earned per hour. If we know that the relationship is proportional, we can write:
y = kx
In this equation, "k" represents the constant of proportionality. It indicates how the amount of money earned changes for every hour worked. To find the value of "k," we need additional information.
For example, if you know that for every 2 hours worked, $10 is earned, we can substitute this information into the equation:
10 = k * 2
To solve for "k," we can divide both sides by 2:
k = 10/2 = 5
Now we have determined that "k" is 5. The equation representing the proportional relationship between hours worked (x) and money earned (y) can be written as:
y = 5x