Question

The table describes the coordinates of several points on a graph. They form a proportion.

What characteristic of the values in the table shows that they form a proportion?
A. Both columns include both positive and negative numbers.
B. The numbers in the x column increase by a constant amount.
C. Each number in the x column relates to only one number in the y column.
D. Every number in the x column can be multiplied by the same value to get the number in the y column.

Answer 1

d

Explanation:

got it right on the test

Answer 2

D. Every number in the x column can be multiplied by the same value to get the number in the y column.

Explanation:

A proportion is the equivalence betweent two rations.

In this case, if the table shows a proportion between variables, they must have a constant ratio of change. In other words, both variables must have a ratio that is constant to each pair. To know if such constant ratio exists, we just have to divide.

However, it's easier if we multiply a factor to x-values to obtain y-values. You can observe that if we multiply
`(1)/(2)` with each x-values, we will obtain each y-value pair.

`-2 * (1)/(2)=-1 \\0 * (1)/(2)=0\\2 * (1)/(2) =1\\4 * (1)/(2)=2`

You can see that if we multiply the same number, we obtain the y-column, that meanst 1/2 is the ratio that relates this variable.

Therefore, the right answer is D.

When we have to variables related by a specific proportion, one of them can increase by a constant amount, but that not necessarily ensure that there is a proportion. It must exist a constant ratio to call that a proportion.