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?

Question image

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.
Answer for screen readers

The completed table is:

x y
2 7
3 10.5
4 14
5 17.5

Yes, the relationship is proportional.

Steps to Solve

  1. 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 $x = 5$:
    $$ y = \frac{7}{2} \cdot 5 = \frac{35}{2} = 17.5 $$

  1. Complete the Table

Fill in the table with the calculated values:

x y
2 7
3 10.5
4 14
5 17.5
  1. 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.
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