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.

Question

contestada

Respuesta :

isyllus isyllus · Answer 1 · 2020-08-14T05:24:34+02:00

Answer:

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([tex]y = x+c[/tex]) 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.

[tex]y = x+1[/tex]

where [tex]y[/tex] represents the parts of water in the solution and

[tex]x[/tex] represents the parts of vinegar in the solution.