Y-Intercept Calculator
Where a Line Crosses the Vertical Axis
The y-intercept is the value of y when x equals zero — the point where a line crosses the vertical axis on a standard graph. Given any two points on a line, this calculator first derives the slope, then works backward to find that crossing point, handling the edge cases of a vertical line (no defined y-intercept unless the line is the y-axis itself) explicitly.
The Formula
m = (y2−y1) / (x2−x1)
b = y1 − m×x1
b = y1 − m×x1
Once the slope (m) is known, the y-intercept (b) is found by substituting one of the known points back into the line equation y = mx + b and solving for b.
Where the Y-Intercept Is Used
- Linear equation modeling — the y-intercept represents the starting value before any change occurs, such as a fixed cost before variable costs are added.
- Break-even analysis — fixed costs in a cost equation appear as the y-intercept of the total cost line.
- Graphing linear functions — the y-intercept is one of the two reference points (with slope) needed to sketch a line quickly.
| Point 1 | Point 2 | Slope | Y-Intercept |
|---|---|---|---|
| (1, 2) | (4, 8) | 2 | 0 |
| (2, 3) | (5, 9) | 2 | −1 |
How to Use This Calculator
- Enter X1 and Y1 for the first point.
- Enter X2 and Y2 for the second point.
- Select Calculate to see the y-intercept (and a note if the line is vertical).
Related Calculations
Need the slope by itself, or where this line crosses the x-axis? See the Slope Calculator and the X-Intercept Calculator.