Question

7. Is it proportional?

8. If so, what is the constant of
proportionality? (unit rate)
9. Write an equation that
expresses the table in the
form
Y= KX

Answer 1

A unit rate is the rate of change in a relationship where the rate is per 1.

The rate of change is the ratio between the x and y (or input and output) values in a relationship. Another term for the rate of change for proportional relationships is the constant of proportionality.

If the rate of change is yx, then so is the constant of proportionality. To simplify things, we set yx=k, where k represents the constant of proportionality.

If you solve a yx=k equation for y, (like this: y=kx), it is called a direct variation equation. In a direct variation equation, y varies directly with x. When x increases or decreases, y also increases or decreases by the same proportion.

To find y in a direct variation equation, multiply x by the constant of proportionality, k.

For example: Given the relationship y=7x, the constant of proportionality k=7, so if x=3, then y=3×7 or 21.

Given the same relationship, if x=7, then y=7×7, or 49.

Explanation:

Answer 2

Yes it is. Y=2.5x

Explanation:

So, lets start with bthe first values of the table and work our way down:

2x=5y

Lets just divide both sides by the 2:

x=5/2y

This means that for every 1 x, there should be 5/2y's.

Or, for every 1 x, there should be 2.5ys.

Lets check the next few to see if thats correct:

3x=7.5y

Divide both sides by 3:

x=7.5/3

This means for every one x, there are again, 2.5ys.

Lets check one more just to be sure:

4x=10y

Divide both sides by 4:

x=10/4

This means for everyone one x, y equals 2.5ys, yet again,

So we can conclude that the poprotional relationship between x and y is:

When x equals 1, y=2.5

Or

Y=2.5x

Hope this helps!