Ask a New Question
Menu

Step 1: 5 = negative 2 (negative StartFraction 3 Over 10 EndFraction) + b. Step 2: 5 = StartFraction 6 Over 10 EndFraction + b. Step 3: 5 minus StartFraction 6 Over 10 EndFraction = StartFraction 6 Over 10 EndFraction minus StartFraction 6 Over 10 EndFraction + b. Step 4: StartFraction 50 Over 10 EndFraction minus StartFraction 6 Over 10 EndFraction = b. Step 5: StartFraction 44 Over 10 EndFraction = b. Step 6: y = negative 2 x minus 4.4.

A student used the slope-intercept form to write the equation of a line that has a slope of -2 and passes through the point (StartFraction negative 3 Over 10 EndFraction, 5). The student’s work is shown to the left.

Analyze the steps to identify the error.
Step1: student switched the x and y values
Step 3: student needed to add StartFraction 6 Over 10 EndFraction to both sides
Step 5: student subtracted incorrectly
Step 6: student needed to add the b value

1 answer

Let's analyze the student's work step by step to identify where the error occurred:

  1. 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).

  2. 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.

  3. 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.

  4. 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.

  5. 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.

  6. 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.