What is the x-intercept of the graph of y = -15x + 60 in the xy-plane?

1. TRANSLATE the problem information

• Given: Linear equation \(\mathrm{y = -15x + 60}\)
• Need to find: x-intercept of the graph
• Key insight: The x-intercept is where the graph crosses the x-axis, which means \(\mathrm{y = 0}\)

2. TRANSLATE the x-intercept condition

• Set \(\mathrm{y = 0}\) in the equation: \(\mathrm{0 = -15x + 60}\)
• This gives us a linear equation to solve for x

3. SIMPLIFY to solve for x

• Starting with: \(\mathrm{0 = -15x + 60}\)
• Add 15x to both sides: \(\mathrm{15x = 60}\)
• Divide both sides by 15: \(\mathrm{x = 4}\)

4. Express as coordinate point

• The x-intercept occurs at \(\mathrm{x = 4}\)
• Since we're on the x-axis, \(\mathrm{y = 0}\)
• Therefore, the x-intercept is \(\mathrm{(4, 0)}\)

Answer: C. (4, 0)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Confusing x-intercept with y-intercept

Students sometimes think "intercept" means where the line crosses the y-axis, so they look for the y-intercept instead. In \(\mathrm{y = -15x + 60}\), when \(\mathrm{x = 0}\), we get \(\mathrm{y = 60}\).

This leads them to select Choice B. \(\mathrm{(0, 60)}\)

Second Most Common Error:

Poor SIMPLIFY execution: Making sign errors during algebraic manipulation

When solving \(\mathrm{0 = -15x + 60}\), students might subtract 60 from both sides to get \(\mathrm{-60 = -15x}\), then divide by -15 incorrectly, getting \(\mathrm{x = -4}\) instead of \(\mathrm{x = 4}\).

This may lead them to select Choice A. \(\mathrm{(-4, 0)}\)

The Bottom Line:

The key challenge is correctly TRANSLATING what "x-intercept" means (\(\mathrm{y = 0}\)) rather than confusing it with y-intercept (\(\mathrm{x = 0}\)). Once that translation is correct, the algebra is straightforward.