One cleaning solution uses 1 part vinegar with 2 parts water. Other cleaning solution uses 2 parts vinegar with 3 parts water. A student says that this represents a proportional relationship because, in each solution, there is one more part of water than vinegar. What is the error and correct it.

Linear relationship.

Step-by-step explanation:

Given that:

Cleansing solution 1 uses 1 part of vinegar with 2 parts water.

Ratio of vinegar to water = 1:2

Cleansing solution 2 uses 2 part of vinegar with 3 parts water.

Ratio of vinegar to water = 2:3

As per a student, the relationship is proportional.

First of all, let us learn about a proportional relationship.

A proportional relationship is the relationship in which the ratios are equal.

OR

In other words, one variable is always a constant value times higher than the other variable.

Here, we have the ratios as 1:2 and 2:3.

One ratio is 0.5 and other ratio is 0.67 which are not equal.

So, it is not proportional relationship.

As we see there is difference of 1 in each ratio.

i.e. Difference in First solution = 2 - 1 = 1

Difference in Second solution = 3 - 2 = 1

So, there is only a constant value change()  in the other variable when one variable changes by 1.

So, it can be called Linear relationship and this constant is 1.

The equation can be represented as.

where represents the parts of water in the solution and

represents the parts of vinegar in the solution.

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step-by-step explanation:

2 x t divided by n

step-by-step explanation: