Question

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

Answer 1

Answer:

The table shows a proportional relationship: YES

The constant of proportionality is k=7

y = 7x

Step-by-step 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:

$\displaystyle k=\frac{y}{x}$

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:

$\displaystyle k=\frac{63}{9}=7$

$\displaystyle k=\frac{28}{4}=7$

$\displaystyle k=\frac{14}{2}=7$

$\displaystyle k=\frac{77}{11}=7$

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