To determine the type of relationship between the x and y values, we can examine the values presented:
- x values: 5.5, 6.4, 7.7
- y values: 33, 38.4, 46.2
We can check the pattern in y-values relative to x-values.
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Calculate the difference in y values and the difference in x values:
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Between the first and second points:
- \( y: 38.4 - 33 = 5.4 \)
- \( x: 6.4 - 5.5 = 0.9 \)
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Between the second and third points:
- \( y: 46.2 - 38.4 = 7.8 \)
- \( x: 7.7 - 6.4 = 1.3 \)
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Now calculate the slopes between these points:
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Slope between the first and second points: \(\frac{5.4}{0.9} = 6\)
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Slope between the second and third points: \(\frac{7.8}{1.3} \approx 6\)
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The slopes are approximately constant. This suggests a linear relationship, as the changes in y are proportional to the changes in x.
Therefore, the type of relationship that exists between the x and y values is:
Linear (First option).
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