Use the equation y = 7/2 x to complete the following table. Is there a proportional relationship between the values of y and x in the table above?

Understand the Problem

The question is asking to use the equation y = (7/2)x to complete the table with specific x values and determine if there is a proportional relationship between y and x.

Answer

The table is completed as follows: | x | y | |-----|-------| | 2 | 7 | | 3 | 10.5 | | 4 | 14 | | 5 | 17.5 | Yes, the relationship is proportional.

Steps to Solve

Calculate Values of y for Each x

To complete the table, substitute the given values of $x$ into the equation $y = \frac{7}{2}x$.

For $x = 2$:
$$ y = \frac{7}{2} \cdot 2 = 7 $$
For $x = 3$:
$$ y = \frac{7}{2} \cdot 3 = \frac{21}{2} = 10.5 $$
For $x = 4$:
$$ y = \frac{7}{2} \cdot 4 = 14 $$
For $x = 5$:
$$ y = \frac{7}{2} \cdot 5 = \frac{35}{2} = 17.5 $$

Complete the Table

Fill in the table with the calculated values:

x	y
2	7
3	10.5
4	14
5	17.5

Determine the Proportional Relationship

To check if there is a proportional relationship between $y$ and $x$, we need to see if the ratio $\frac{y}{x}$ remains constant.

Calculate the ratios:
- For $x = 2, y = 7$:
  $$ \frac{y}{x} = \frac{7}{2} = 3.5 $$
- For $x = 3, y = 10.5:
  $$ \frac{y}{x} = \frac{10.5}{3} = 3.5 $$
- For $x = 4, y = 14:
  $$ \frac{y}{x} = \frac{14}{4} = 3.5 $$
- For $x = 5, y = 17.5:
  $$ \frac{y}{x} = \frac{17.5}{5} = 3.5 $$

Since the ratios are all equal, there is a proportional relationship.

The completed table is:

x	y
2	7
3	10.5
4	14
5	17.5

Yes, the relationship is proportional.

More Information

The relationship $y = \frac{7}{2}x$ indicates that $y$ increases linearly as $x$ increases. The constant ratio $\frac{y}{x} = 3.5$ confirms proportionality. In proportion, as $x$ doubles, $y$ also doubles.

Tips

Forgetting to multiply correctly when substituting $x$ into the equation.
Miscalculating the ratios when checking for proportionality. Always simplify the ratios carefully.

Thank you for voting!