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

The equation of the line given is \(2x - 3y = 6\). To find the point where this line intersects the x-axis, we set \(y = 0\) because any point on the x-axis has a zero y-coordinate.

Substitute \(y = 0\) in the equation:

\(2x - 3(0) = 6\)

\(2x = 6\)

Now solve for \(x\):

\(x = \frac{6}{2} = 3\)

Thus, the line intersects the x-axis at the point \((3, 0)\).

This matches the correct answer: (3, 0).