Question

Is the following double line diagram correctly? use complete sentences to explain your reasoning

Answer 1

We will investigate how to validate double number lines.

A double number line is used to express a relation between two linear quantities. This relationship is expressed by a linear constant ( k ).

The ratio between each and every quantity must remains same or equal to the linear constant ( k ).

A double number line is expressed as two number lines with divisions spaced apart equally. However, the numerical value of each division may vary across the two lines.

To determine the validity of the double number line we need to ensure that a constant prportionality is conserved. This conservation of proportionality is represented by a constant ratio ( k ) for each induvidual entry/division value.

Therefore,

`k\text{ = }\frac{Top\text{ division number}}{Bottom\text{ division number}}`

We will determine the ratio of proportionality of each dvision across the two lines and see whether they are constant or not.

So,

`(5)/(3)\ldots\text{ First division}`

Then,

`(10)/(8)=(5)/(4)\ldots\text{ Second division}`

Then,

`(20)/(16)=(5)/(4)\ldots\text{ Third division}`

And so on...

We see from above that the ratio of first division is not equal to the ratio of second or thrid division. Hence, the proportionaility is not constant. It changed between first and second division. Hence, the double number line represented is NOT a valid one because the proportionaility ratio is NOT constant for each entry.