Question

The equation y=5x represents the relationship between the number of gallons of water used (y) and the number of minutes (x) for most showerheads manufactured before 1994. Explain why the relationship is proportional. Describe the relationship in words

Answer 1

• The relationship is proportional, because it has the form of a Direct proportion equation, hence it is a straight line that passes through the origin.
• The number of gallons of water used is directly porportional to the number of minutes for most showerheads manufactured before 1994 (Most howerheads that were manufactures before 1994 use 5 gallons of water per minute).

Explanation:

The equation
`y = mx` represents a straight line that passes through the origin, with slope "m".

Direct proportion equations have the following form:

`y=kx`

Where "k" is called the "Constant of proportionality".

Therefore, by definition, a proportional relationship is a straight line that passes through the origin.

In this case, given the equation:

`y=5x`

You can identify that it has the form of Direct proportion equation (
`y=kx`).

Observe that the constant of proportionality is the following:

`k=5`

Therefore, you can conclude that the relationship is proportional and can be described as:

The number of gallons of water used is directly porportional to the number of minutes for most showerheads manufactured before 1994.

This means that most showerheads that were manufactures before 1994 use 5 gallons of water per minute