Question

.........??????????????

Answer 1

The table shows a proportional relationship: YES

The constant of proportionality is k=7

y = 7x

Explanation:

Proportions

A direct proportion is a relation between variables where their ratio is a constant value. This means that if y and x are proportional, then:

y = kx

Where k is the constant of proportionality. It can be calculated by solving the equation for k:

`\displaystyle k=(y)/(x)`

We are given a table with 4 pairs of values. If the relationship between the variables is proportional, then the ratio y/x should be constant.

Let's verify some points:

`\displaystyle k=(63)/(9)=7`

`\displaystyle k=(28)/(4)=7`

`\displaystyle k=(14)/(2)=7`

`\displaystyle k=(77)/(11)=7`

Since all the ratios are equal,

The table shows a proportional relationship: YES

The constant of proportionality is k=7

The equation for the relationship is

y = 7x