What is the x-intercept of the line given by \(2x-3y=12\)?
6
The x-intercept of a straight line is the point where the line crosses the x-axis, and every point on the x-axis has a y-coordinate of zero.
So to find the x-intercept, set \(y = 0\) in the equation of the line.
The line is \(2x - 3y = 12\); putting \(y = 0\) gives \(2x - 3(0) = 12\).
This simplifies to \(2x = 12\).
Dividing both sides by 2: \(x = \dfrac{12}{2} = 6\).
So the line meets the x-axis at the point \((6, 0)\), and the x-intercept is the value 6.
Key concept: x-intercept is found by substituting \(y = 0\); a y-intercept would instead need \(x = 0\).
The x-intercept is 6.
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