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The proportional relationship for the earnings and hours worked for Employee 1 is displayed in the table. The proportional relationship between the earnings and hours worked for Employee 2 is displayed in the graph. What is the equation that represents the proportional relationship between the earnings and hours worked for Employee 1 and Employee 2?…

The dot is at. 5,75

3 answers

To find the equation that represents the proportional relationship, we need to understand the concept of proportionality. In a proportional relationship, the earnings (y) are directly proportional to the hours worked (x). This means that we can express this relationship as:

\[ y = kx \]

where \( k \) is the constant of proportionality.

For Employee 1:

Since the specifics of the table for Employee 1 are not provided, we cannot extract the constant \( k_1 \) directly. However, we can assume the relationship can be described with some value based on the data in the table.

For Employee 2:

You mentioned that there is a dot at (5, 75) on the graph for Employee 2. This suggests that when Employee 2 works 5 hours, they earn $75. Using this information, we can find \( k_2 \).

From the point (5, 75): \[ 75 = k_2 \cdot 5 \] To solve for \( k_2 \): \[ k_2 = \frac{75}{5} = 15 \]

So, the equation for Employee 2 is: \[ y = 15x \]

Conclusion

For Employee 2, the equation is: \[ y = 15x \]

Without the specific data for Employee 1, you would need to find the constant \( k_1 \) based on the table provided for Employee 1. Once you have that value, you can also express the equation for Employee 1 in the same form as \( y = k_1 x \).

The first dot is at 0,0
The second dot is at 1,15
The third dot is at 3,45
The forth dot is at 5,75

Based on the points you've provided for Employee 1, we can analyze the proportional relationship between the earnings and hours worked.

The points for Employee 1 are:

  • (0, 0)
  • (1, 15)
  • (3, 45)
  • (5, 75)

Finding the Constant of Proportionality for Employee 1

We can see that the earnings (y) are directly proportional to the hours worked (x). Let's check the relationship at one of the points.

Using the point (1, 15): \[ 15 = k_1 \cdot 1 \implies k_1 = 15 \]

Now let's verify this with the other points:

  • For (3, 45): \[ 45 = k_1 \cdot 3 \implies k_1 = \frac{45}{3} = 15 \]

  • For (5, 75): \[ 75 = k_1 \cdot 5 \implies k_1 = \frac{75}{5} = 15 \]

In all cases, we find that \( k_1 = 15 \). Therefore, the equation for Employee 1 is: \[ y = 15x \]

For Employee 2

From your earlier information, the equation that we derived for Employee 2, based on the point (5, 75), was: \[ y = 15x \]

Conclusion

Both Employee 1 and Employee 2 have the same proportional relationship between earnings and hours worked:

\[ y = 15x \]

This indicates that both employees earn $15 for every hour worked.