Question

Which of the following curve/straight line equations will pass through the origin when plotted on a graph?

• A. \( \frac{x}{2} + \frac{y}{2} = 0 \)
• B. \( 1 + y + x = 1 \)
• C. \( x y = 1 \)
• D. \( 2y - 2x + 2 = 0 \)

Hint:

To check if an equation passes through the origin, substitute \( x = 0 \) and \( y = 0 \). If the equation holds, it passes through the origin.

Answer 1

The Correct Option is A, B

Step 1: Understanding equations passing through the origin. 
For an equation to pass through the origin, when \( x = 0 \) and \( y = 0 \), the equation should hold true. Let's check the options: 
 

Step 2: Analyzing the options. 
- (A) \( \frac{x}{2} + \frac{y}{2} = 0 \): If \( x = 0 \) and \( y = 0 \), this equation holds true. 

- (B) \( 1 + y + x = 1 \): This equation holds true when \( x = 0 \) and \( y = 0 \). 

- (C) \( x y = 1 \): This equation does not hold true when \( x = 0 \) and \( y = 0 \). 

- (D) \( 2y - 2x + 2 = 0 \): This equation does not hold true when \( x = 0 \) and \( y = 0 \). 
 

Step 3: Conclusion. 
The correct answer is:

(A) \( \frac{x}{2} + \frac{y}{2} = 0 \)

(B) \( 1 + y + x = 1 \)