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:
[tex]\displaystyle k=\frac{y}{x}[/tex]
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:
[tex]\displaystyle k=\frac{63}{9}=7[/tex]
[tex]\displaystyle k=\frac{28}{4}=7[/tex]
[tex]\displaystyle k=\frac{14}{2}=7[/tex]
[tex]\displaystyle k=\frac{77}{11}=7[/tex]
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
