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y = 5, 9, 10, 10.5, 11.

x = 1, 2, 3, 4, 5.

у = 1.35x + 5.05
У = x+5
y =5x + 11
у = 5.05x + 1.35

1 answer

It looks like you've provided a set of \(y\) values and corresponding \(x\) values, along with several equations.

  1. Data Points: \[ y = [5, 9, 10, 10.5, 11] \] \[ x = [1, 2, 3, 4, 5] \]

  2. Equations:

    • \(y = 1.35x + 5.05\)
    • \(y = x + 5\)
    • \(y = 5x + 11\)
    • \(y = 5.05x + 1.35\)

To analyze these equations with respect to the given data points, let's calculate the \(y\) values for each equation at the \(x\) values from 1 to 5.

Calculating \(y\) values for each equation:

  1. For \(y = 1.35x + 5.05\):

    • \(x = 1\) → \(y = 1.35(1) + 5.05 = 6.4\)
    • \(x = 2\) → \(y = 1.35(2) + 5.05 = 7.75\)
    • \(x = 3\) → \(y = 1.35(3) + 5.05 = 9.1\)
    • \(x = 4\) → \(y = 1.35(4) + 5.05 = 10.45\)
    • \(x = 5\) → \(y = 1.35(5) + 5.05 = 11.8\)

  2. For \(y = x + 5\):

    • \(x = 1\) → \(y = 1 + 5 = 6\)
    • \(x = 2\) → \(y = 2 + 5 = 7\)
    • \(x = 3\) → \(y = 3 + 5 = 8\)
    • \(x = 4\) → \(y = 4 + 5 = 9\)
    • \(x = 5\) → \(y = 5 + 5 = 10\)

  3. For \(y = 5x + 11\):

    • \(x = 1\) → \(y = 5(1) + 11 = 16\)
    • \(x = 2\) → \(y = 5(2) + 11 = 21\)
    • \(x = 3\) → \(y = 5(3) + 11 = 26\)
    • \(x = 4\) → \(y = 5(4) + 11 = 31\)
    • \(x = 5\) → \(y = 5(5) + 11 = 36\)

  4. For \(y = 5.05x + 1.35\):

    • \(x = 1\) → \(y = 5.05(1) + 1.35 = 6.4\)
    • \(x = 2\) → \(y = 5.05(2) + 1.35 = 11.45\)
    • \(x = 3\) → \(y = 5.05(3) + 1.35 = 16.50\)
    • \(x = 4\) → \(y = 5.05(4) + 1.35 = 21.55\)
    • \(x = 5\) → \(y = 5.05(5) + 1.35 = 26.60\)

Summary of Results:

Let’s summarize the evaluated \(y\) values for easy comparison:

| \(x\) | Observed \(y\) | \(y = 1.35x + 5.05\) | \(y = x + 5\) | \(y = 5x + 11\) | \(y = 5.05x + 1.35\) | |-------|----------------|-----------------------|----------------|------------------|-----------------------| | 1 | 5 | 6.4 | 6 | 16 | 6.4 | | 2 | 9 | 7.75 | 7 | 21 | 11.45 | | 3 | 10 | 9.1 | 8 | 26 | 16.50 | | 4 | 10.5 | 10.45 | 9 | 31 | 21.55 | | 5 | 11 | 11.8 | 10 | 36 | 26.60 |

Conclusion:

  • The equation \(y = 1.35x + 5.05\) fits relatively well for \(x = 1, 2, 4\) and closely matches the observed \(y\) values for those points.
  • The equation \(y = x + 5\) is fairly linear but underestimates the observed \(y\) values.
  • The equation \(y = 5x + 11\) significantly overestimates all values.
  • The equation \(y = 5.05x + 1.35\) also overestimates \(y\) values significantly.

If you need further analysis or specific interpretations of these equations or any other insights, let me know!