x-intercept – Where a Line Crosses the x-axis
The x-intercept of a line is the point where it crosses the x-axis. At that exact point, the line's height above or below the x-axis is zero – in other words, y = 0. This one fact is the entire trick to finding any x-intercept: substitute y = 0 into the line's equation and solve for x.
x-intercepts show up constantly whenever a graph represents something crossing from positive to negative – profit turning into loss, height reaching ground level, or a tank's water level hitting zero – which is exactly why this skill matters well beyond pure algebra.
Finding an x-intercept
At the x-intercept, y = 0. Substitute y = 0 into the line's equation and solve for x.
Set y = 0: 0 = 3x − 12, so 3x = 12, giving x = 4. The x-intercept is the point (4, 0).
Real-Life Application
- Break-even analysis: the x-intercept of a profit line shows the break-even point.
- Physics: a falling object's height graph crosses the x-axis when it hits the ground.
- Chemistry: reaction-rate graphs use intercepts to mark when a reaction stops.
Key Takeaways
- The x-intercept is where a line crosses the x-axis, where y = 0.
- Substitute y = 0 into the equation and solve for x to find it.
- A point lies on the x-axis only when its y-coordinate is exactly 0.
Practice: x-intercept
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