Question

Which type of straight line will be the graph of \( x - y = 0 \)?

• A. Parallel to \(x\)-axis
• B. Parallel to \(y\)-axis
• C. Passing through origin
• D. None of these

Hint:

If a line can be written as \(y=mx\) (no constant term), it always passes through the origin. A constant \(c\) in \(y=mx+c\) shifts it off the origin.

Answer 1

The Correct Option is C

Step 1: Rearrange the equation.
\(x - y = 0 \;\Rightarrow\; y = x.\) This is a line with slope \(1\).
Step 2: Identify intercept.
When \(x=0\), \(y=0\). Hence the line passes through \((0,0)\), i.e., the origin.
Step 3: Conclude.
Therefore, the graph is a straight line through the origin (making a \(45^\circ\) angle with the positive \(x\)-axis).