The graph of linear equation x + 2y = 2, cuts the y-axis at

Question

The graph of linear equation x + 2y = 2, cuts the y-axis at

1. A. (1,0)
2. B. (2,0)
3. C. (0,1) (Correct answer)
4. D. (0,2)

Correct Answer

Option C — (0,1)

Detailed Solution & Explanation

The correct answer is (0,1).

Key Points

• A graph cuts the y-axis at the point where $x = 0$.
• Substituting $x = 0$ into $x + 2y = 2$:
  • $0 + 2y = 2$
  • $y = 1$
• The y-intercept is therefore (0, 1).

Shortcut Trick

• Any point on the y-axis has $x = 0$; any point on the x-axis has $y = 0$. Options B and D can be rejected on sight for having a non-zero first coordinate — they are x-axis points.

Additional Information

• The x-intercept of the same line: set $y = 0$ → $x = 2$, giving (2, 0). This is exactly option B, placed as the trap for candidates who zero the wrong variable.
• Intercept form: rewriting $x + 2y = 2$ as $\frac{x}{2} + \frac{y}{1} = 1$ shows the intercepts directly — $a = 2$ on the x-axis, $b = 1$ on the y-axis.
• Memory aid: "y-axis, x is zero" — the axis you are meeting is the variable that survives.