Question

In the following equations, the line passing through (0, 0) is

• A. y=mx
• B. y=mx-c
• C. y=mx+c
• D. y=c

Answer 1

The Correct Option is A

Step 1: To determine if a line passes through the origin \((0, 0)\), we substitute \(x = 0\) into the equation and check if \(y = 0\).

Step 2: Let's evaluate each option:
Option (1): \(y = mx\)
Put \(x = 0\): \(y = m \cdot 0 = 0\)
Hence, the line passes through the origin. ✅

Option (2): \(y = mx - c\)
Put \(x = 0\): \(y = 0 - c = -c\)
Hence, the line passes through the point \((0, -c)\), not the origin. ❌

Option (3): \(y = mx + c\)
Put \(x = 0\): \(y = 0 + c = c\)
Hence, the line passes through \((0, c)\), not the origin. ❌

Option (4): \(y = c\)
This represents a horizontal line at height \(c\), and it passes through the origin only when \(c = 0\), which is not guaranteed. ❌

Step 3: Therefore, the only line that definitely passes through \((0, 0)\) is: \(y = mx\)