Question

The graphs of the equations \(2x - y - 3 = 0\) and \(12x + 7y - 5 = 0\) are which type of straight lines?

• A. Coincident straight lines
• B. Parallel straight lines
• C. Intersecting straight lines
• D. None of these

Hint:

In 2D, two non-vertical lines: equal slopes \(\Rightarrow\) parallel; equal slopes and equal intercepts \(\Rightarrow\) coincident; unequal slopes \(\Rightarrow\) intersecting.

Answer 1

The Correct Option is C

Step 1: Convert each equation to slope–intercept form \(y=mx+c\).
For \(2x - y - 3 = 0 \Rightarrow y = 2x - 3\), slope \(m_1 = 2\).
For \(12x + 7y - 5 = 0 \Rightarrow 7y = -12x + 5 \Rightarrow y = -\dfrac{12}{7}x + \dfrac{5}{7}\), slope \(m_2 = -\dfrac{12}{7}\).
Step 2: Compare slopes.
Since \(m_1 \neq m_2\) (\(2 \neq -\dfrac{12}{7}\)), the lines are neither parallel nor coincident; hence they intersect.
Step 3: Conclude.
Therefore, the two given lines are intersecting straight lines.