Let's analyze the student's work step by step to identify where the error occurred:
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Step 1: 5 = negative 2 (negative StartFraction 3 Over 10 EndFraction) + b.
- This step is correct. The equation is being set up using the point (−3/10, 5) and the slope (-2).
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Step 2: 5 = StartFraction 6 Over 10 EndFraction + b.
- This step is also correct. The calculation of negative 2 multiplied by negative 3/10 gives 6/10.
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Step 3: 5 minus StartFraction 6 Over 10 EndFraction = StartFraction 6 Over 10 EndFraction minus StartFraction 6 Over 10 EndFraction + b.
- Here, the student should have added 6/10 to both sides to isolate \( b \). Hence, this step is incorrect.
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Step 4: StartFraction 50 Over 10 EndFraction minus StartFraction 6 Over 10 EndFraction = b.
- This step comes from carrying out the subtraction but only makes sense if the previous step had been performed correctly. Since Step 3 was incorrect, this results in an equation that is misleading, yet the math in this step is numerically valid.
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Step 5: StartFraction 44 Over 10 EndFraction = b.
- This follows from Step 4 and although it is mathematically correct for the operation done, since Step 3 was erroneous, it leads to an incorrect conclusion.
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Step 6: y = negative 2 x minus 4.4.
- The final equation isn't reflective of the correct y-intercept. It should be \( b = \frac{44}{10} = 4.4 \), and thus, it should be \( y = -2x + 4.4 \).
Conclusion:
- The main error in the student's work occurs in Step 3 where they needed to add \( \frac{6}{10} \) to both sides to isolate \( b \). Hence, the correct response to identify the error is: Step 3: student needed to add StartFraction 6 Over 10 EndFraction to both sides.