y = 70x + 8 Which table gives three values of x and their corresponding values of y for the...

1. TRANSLATE the problem information

• Given information:
  • Linear equation: \(\mathrm{y = 70x + 8}\)
  • Four tables with x values (0, 2, 4) and corresponding y values
  • Need to find which table correctly matches the equation

• What this tells us: I need to substitute each x value into the equation and check if the calculated y matches the table's y value.

2. INFER the approach

• Strategy: Test each table systematically by substituting x values
• Start with Choice A and work through each x value
• If all three pairs work, that's the answer; if any pair fails, move to next choice

3. SIMPLIFY the calculations for Choice A

• When \(\mathrm{x = 0}\): \(\mathrm{y = 70(0) + 8}\)
  \(\mathrm{= 0 + 8}\)
  \(\mathrm{= 8}\) ✓ (matches table)
• When \(\mathrm{x = 2}\): \(\mathrm{y = 70(2) + 8}\)
  \(\mathrm{= 140 + 8}\)
  \(\mathrm{= 148}\) ✓ (matches table)
• When \(\mathrm{x = 4}\): \(\mathrm{y = 70(4) + 8}\)
  \(\mathrm{= 280 + 8}\)
  \(\mathrm{= 288}\) ✓ (matches table)

4. Verify Choice A is complete

• All three coordinate pairs work perfectly
• No need to check other choices since Choice A is confirmed correct

Answer: A

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak SIMPLIFY execution: Students make arithmetic errors during the multiplication or addition steps.

For example, calculating \(\mathrm{y = 70(2) + 8}\) as 132 instead of 148 (forgetting to add the 8, or miscalculating \(\mathrm{70×2}\)). This type of error might lead them to select Choice D (which has 132 for x=2), since that choice has the correct y-value for x=0 but wrong calculations for the other values.

Second Most Common Error:

Poor TRANSLATE reasoning: Students mix up what to substitute where, or confuse the given equation with a different linear relationship.

Some students might accidentally think the pattern should be \(\mathrm{y = 4x + 70}\) (switching the coefficient and constant), which would produce the values in Choice B (70, 78, 86). This shows they understand the substitution process but translated the original equation incorrectly.

The Bottom Line:

This problem tests careful arithmetic execution more than complex reasoning. The conceptual understanding is straightforward, but students need to maintain accuracy through multiple calculations to avoid being trapped by answer choices that result from common computational mistakes.