Question

Find the equation of a line passing through the intersection of \( 3x + y - 4 = 0 \) and \( x - y = 0 \), and making a \( 45^\circ \) angle with \( x - 3y + 5 = 0 \).

• A. \( x + y = 2 \)
• B. \( x + 2y = 3 \)
• C. \( 4x + 3y = 7 \)
• D. \( x + 3y = 4 \)

Hint:

For angles between lines, use slope transformation formulas.

Answer 1

The Correct Option is B

Step 1: Find Intersection Point
Solving \( 3x + y - 4 = 0 \) and \( x - y = 0 \), we get: \[ x = y, \quad 3x + x - 4 = 0 \Rightarrow x = 1, y = 1 \] Step 2: Finding Equation of Line
Using angle condition: \[ m_1 = \frac{\text{change in y}}{\text{change in x}} \] \[ x + 2y = 3 \] Thus, the correct answer is \( x + 2y = 3 \).