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The table below shows the amount that must be repaid, y, when x dollars are borrowed.Amount BorrowedAmount Repaid$100$120$200$240$500$600$800$960NOTE: In the bottom right corner of each question, you will see an option to check answer. Click this to check your answer before moving on to the next question. It will not tell you the correct answer, but it will tell you if the answer you selected is correct. You can use this feature twice per question.(1 point)Responsesy=65x+10y is equal to 6 fifths x plus 10y=56x+10y is equal to 5 sixths x plus 10y=56xy is equal to 5 sixths xy=65xy is equal to 6 fifths xSkip to navigation

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To analyze the given amounts borrowed and the corresponding amounts repaid, we can express the relationship between the amounts borrowed (x) and the amounts repaid (y) as a linear equation.

From the provided data:

  • When $100 is borrowed, $120 is repaid.
  • When $200 is borrowed, $240 is repaid.
  • When $500 is borrowed, $600 is repaid.
  • When $800 is borrowed, $960 is repaid.

We can see that the amount repaid (y) is proportional to the amount borrowed (x).

Let’s calculate the ratio for some of the pairs:

  1. For $100 borrowed: \[ \frac{120}{100} = 1.2 \]

  2. For $200 borrowed: \[ \frac{240}{200} = 1.2 \]

  3. For $500 borrowed: \[ \frac{600}{500} = 1.2 \]

  4. For $800 borrowed: \[ \frac{960}{800} = 1.2 \]

This indicates that the amount repaid (y) is 1.2 times the amount borrowed (x).

We can represent this relationship as: \[ y = 1.2x \]

Now, let's rewrite this relationship in a different form: To express 1.2 as a fraction, we can write: \[ 1.2 = \frac{12}{10} = \frac{6}{5} \] Thus, we have: \[ y = \frac{6}{5}x \]

Let's check the options presented in terms of y:

  1. \(y = 65x + 10\) - Incorrect.
  2. \(y\) is equal to \(6/5x + 10\) - Incorrect.
  3. \(y = 56x + 10\) - Incorrect.
  4. \(y\) is equal to \(5/6x + 10\) - Incorrect.
  5. \(y = 56x\) - Incorrect.
  6. \(y\) is equal to \(5/6y\) - Incorrect.
  7. \(y\) is equal to \(6/5x\) - Correct.

Hence, the correct response in the context of the mathematical relationship derived from the data provided is: y = 6/5x (Option that represents the relationship of repaid to borrowed).