y = x + 4 Which table gives three values of x and their corresponding values of y for the...

1. TRANSLATE the problem requirements

• Given information:
  • Equation: \(\mathrm{y = x + 4}\)
  • Need to find which table correctly shows x-values and their corresponding y-values

• What this tells us: We need to substitute each x-value from the tables into the equation and check if we get the corresponding y-value shown.

2. SIMPLIFY by testing each table systematically

• Start with Table A and substitute each x-value:
  • When \(\mathrm{x = 0}\): \(\mathrm{y = 0 + 4 = 4}\) (matches table)
  • When \(\mathrm{x = 1}\): \(\mathrm{y = 1 + 4 = 5}\) (matches table)
  • When \(\mathrm{x = 2}\): \(\mathrm{y = 2 + 4 = 6}\) (matches table)

• Since all values match, Table A is correct, but let's verify others are wrong:

3. SIMPLIFY verification for remaining tables

• Table B: When \(\mathrm{x = 0}\), y should be 4, but table shows 6 ✗
• Table C: When \(\mathrm{x = 0}\), y should be 4, but table shows 2 ✗
• Table D: When \(\mathrm{x = 0}\), y should be 4, but table shows 0 ✗

Answer: A

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak SIMPLIFY execution: Students make basic arithmetic errors when substituting values into \(\mathrm{y = x + 4}\).

For example, they might calculate \(\mathrm{y = 0 + 4 = 6}\) instead of 4, or get confused with the order of operations. These calculation mistakes cause them to incorrectly eliminate the right answer or incorrectly validate a wrong table.

This may lead them to select Choice B, C, or D depending on which arithmetic error they make.

The Bottom Line:

This problem tests whether students can systematically apply substitution to verify equation-table relationships. The key is careful arithmetic - the conceptual part is straightforward, but execution errors in basic addition can derail the entire solution.