Question

The line \(2x - 3y = 6\) intersects x-axis at

• A. (0, –2)
• B. (0, 3)
• C. (–2, 0)
• D. (3, 0)

Hint:

To find x-intercept of a line, substitute \(y = 0\) in the equation.

Answer 1

The Correct Option is D

Given:
Equation of the line: \(2x - 3y = 6\)

To find:
Point where the line intersects the x-axis.

Step 1: Use the fact that on x-axis, \(y = 0\)
Substitute \(y = 0\) in the equation:
\[ 2x - 3(0) = 6 \implies 2x = 6 \implies x = 3 \]

Step 2: Write the coordinate of intersection
The line intersects the x-axis at \((3, 0)\).

Final Answer:
\[ \boxed{(3, 0)} \]