y = 3 - x Which table gives three values of x and their corresponding values of y for the...

1. INFER the solution strategy

• Given: Linear equation \(\mathrm{y = 3 - x}\) and four different tables
• Strategy: Test each table by substituting its x values into the equation and checking if the calculated y values match the table's y values
• We need all three pairs in a table to match for it to be correct

2. SIMPLIFY by testing each table systematically

Testing Choice (A):

• \(\mathrm{x = 0}\): \(\mathrm{y = 3 - 0 = 3}\) ✓ (table shows 3)
• \(\mathrm{x = 1}\): \(\mathrm{y = 3 - 1 = 2}\) ✓ (table shows 2)
• \(\mathrm{x = 2}\): \(\mathrm{y = 3 - 2 = 1}\) ✓ (table shows 1)
• All values match!

Testing Choice (B):

• \(\mathrm{x = 0}\): \(\mathrm{y = 3 - 0 = 3}\) ✓ (table shows 3)
• \(\mathrm{x = 1}\): \(\mathrm{y = 3 - 1 = 2}\) ✗ (table shows 4)
• Stop here - this table doesn't match

Testing Choice (C):

• \(\mathrm{x = 0}\): \(\mathrm{y = 3 - 0 = 3}\) ✗ (table shows -3)
• Stop here - this table doesn't match

Testing Choice (D):

• \(\mathrm{x = 0}\): \(\mathrm{y = 3 - 0 = 3}\) ✗ (table shows 0)
• Stop here - this table doesn't match

Answer: A

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak SIMPLIFY execution: Making arithmetic errors in subtraction, especially with the order of operations in "\(\mathrm{3 - x}\)"

Students might calculate incorrectly:

• For \(\mathrm{x = 1}\): Computing "\(\mathrm{1 - 3 = -2}\)" instead of "\(\mathrm{3 - 1 = 2}\)"
• For \(\mathrm{x = 2}\): Computing "\(\mathrm{2 - 3 = -1}\)" instead of "\(\mathrm{3 - 2 = 1}\)"

This confusion about which number to subtract from which may lead them to select Choice (C) (-3, -4, -5) since these match the incorrect calculations.

Second Most Common Error:

Insufficient INFER reasoning: Only checking the first row of each table instead of systematically verifying all three coordinate pairs

Students see that \(\mathrm{x = 0}\) gives \(\mathrm{y = 3}\) in both Choice (A) and Choice (B), then pick one without checking the remaining values. This leads to guessing between these two choices.

The Bottom Line:

This problem requires careful attention to the order of subtraction in "\(\mathrm{3 - x}\)" and systematic verification of all coordinate pairs, not just spot-checking one value.