X and Y Intercepts Calculator
Find where a line crosses the x-axis and y-axis
Graph
Step-by-Step Solution
Understanding Intercepts
X-Intercept
The x-intercept is where the line crosses the x-axis (where y = 0). To find it, set y = 0 and solve for x.
X-intercept point: (x, 0)
Y-Intercept
The y-intercept is where the line crosses the y-axis (where x = 0). To find it, set x = 0 and solve for y.
Y-intercept point: (0, y)
Special Cases
- Horizontal line (y = c): No x-intercept (unless c = 0), y-intercept at (0, c)
- Vertical line (x = c): X-intercept at (c, 0), no y-intercept (unless c = 0)
- Line through origin: Both intercepts are (0, 0)
Frequently Asked Questions
What is an x-intercept?
The x-intercept is the point where a line crosses the x-axis. At this point, y = 0.
What is a y-intercept?
The y-intercept is the point where a line crosses the y-axis. At this point, x = 0.
How do I find intercepts from y = mx + b?
The y-intercept is b (the constant). For the x-intercept, set y = 0 and solve: x = -b/m.
Can a line have no intercepts?
A vertical line (x = c where c ≠ 0) has no y-intercept. A horizontal line (y = c where c ≠ 0) has no x-intercept.
What if both intercepts are at the origin?
If a line passes through the origin (0, 0), then both the x-intercept and y-intercept are at (0, 0).
Why are intercepts useful?
Intercepts provide easy points to plot when graphing. They're also useful in real-world problems, often representing starting values or break-even points.
How do I find intercepts from standard form?
From Ax + By = C: For x-intercept, set y = 0 and get x = C/A. For y-intercept, set x = 0 and get y = C/B.
What's intercept form?
Intercept form is x/a + y/b = 1, where a is the x-intercept and b is the y-intercept. It shows both intercepts directly.