y = -4x + 40 Which table gives three values of x and their corresponding values of y for the...

1. TRANSLATE the problem requirements

• Given information:
  • Linear equation: \(\mathrm{y = -4x + 40}\)
  • Need to find y values when \(\mathrm{x = 0}\), \(\mathrm{1}\), and \(\mathrm{2}\)
• What this means: I need to substitute each x value into the equation and calculate the corresponding y value

2. SIMPLIFY by substituting each x value systematically

For x = 0:

• \(\mathrm{y = -4(0) + 40}\)
• \(\mathrm{y = 0 + 40 = 40}\)

For x = 1:

• \(\mathrm{y = -4(1) + 40}\)
• \(\mathrm{y = -4 + 40 = 36}\)

For x = 2:

• \(\mathrm{y = -4(2) + 40}\)
• \(\mathrm{y = -8 + 40 = 32}\)

3. TRANSLATE results to identify the correct table

• The correct table should show: \(\mathrm{(0,40), (1,36), (2,32)}\)
• Checking each choice, only Choice C matches these values exactly

Answer: C

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak SIMPLIFY skill: Students make sign errors with the negative coefficient, calculating \(\mathrm{y = 4x + 40}\) instead of \(\mathrm{y = -4x + 40}\)

When \(\mathrm{x = 1}\): \(\mathrm{y = 4(1) + 40 = 44}\) (instead of 36)
When \(\mathrm{x = 2}\): \(\mathrm{y = 4(2) + 40 = 48}\) (instead of 32)

This leads them to select Choice B (showing values 44 and 48)

Second Most Common Error:

Poor TRANSLATE reasoning: Students misunderstand the equation structure and ignore the constant term, calculating only \(\mathrm{y = -4x}\)

When \(\mathrm{x = 0}\): \(\mathrm{y = -4(0) = 0}\) (instead of 40)
When \(\mathrm{x = 1}\): \(\mathrm{y = -4(1) = -4}\) (instead of 36)
When \(\mathrm{x = 2}\): \(\mathrm{y = -4(2) = -8}\) (instead of 32)

This causes them to select Choice A (showing values 0, -4, -8)

The Bottom Line:

This problem tests careful attention to both the negative coefficient and the positive constant term. Success requires methodical substitution and accurate arithmetic with signed numbers.