Y-Intercept Calculator — Find b in y = mx + b
Enter the slope m and the coordinates of any known point (x₁, y₁) on the line to find the y-intercept b. The full line equation y = mx + b is shown together with an interactive plot.
The y-value where the line crosses the y-axis (x = 0)
- 1
Slope × x₁
m × x₁ = 2 × 3 = 6 - 2
y-intercept b
y₁ − m·x₁ = 7 − 6 = 1The value of y when x = 0 — where the line crosses the y-axis.
How does this calculator work?
The y-intercept b is where a line crosses the y-axis. Given slope m and a point (x₁, y₁), compute b = y₁ − m · x₁. The full line equation is then y = mx + b, and the x-intercept is x = −b / m (if m ≠ 0). Positive b means the line crosses above the origin; negative b means below.
Formula
How this is calculated
Every non-vertical straight line can be written in slope-intercept form y = mx + b, where m is the slope (rise divided by run) and b is the y-intercept — the value of y where the line crosses the y-axis (i.e. where x = 0). If you know the slope and any point on the line, you can solve for b by substituting x = x₁ and y = y₁ into the equation and rearranging: b = y₁ − m · x₁.
Once b is known the full equation is determined. The x-intercept — where the line crosses the x-axis (y = 0) — is found by setting y = 0: x = −b / m. If the slope is exactly zero the line is horizontal and has no x-intercept unless it lies on the x-axis itself.
This calculator assumes a straight (linear) line. For non-linear curves the intercept concept still applies, but the formula changes depending on the curve. All inputs are unitless real numbers; the y-intercept has the same units as y (whatever they represent in context).
Frequently asked questions
The y-intercept is the value of y when x = 0 — it is where the line crosses the vertical (y) axis. In applications it often represents a starting value or fixed component: for example, in cost models it may be the fixed cost when zero units are produced.
Yes. First calculate the slope from the two points: m = (y₂ − y₁) / (x₂ − x₁). Then use b = y₁ − m · x₁ as usual. Many slope calculators on this site compute m for you; paste it here along with either point.
A zero slope means the line is horizontal: y = b everywhere. The y-intercept equals y₁ (since y is the same at every x), and there is no x-intercept — unless b = 0, in which case the line lies on the x-axis.
Also known as
TG we-Calculate Editorial Team. (2026). Y-Intercept Calculator — Find b in y = mx + b [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/y-intercept-calculator
TG we-Calculate Editorial Team. "Y-Intercept Calculator — Find b in y = mx + b." TG we-Calculate. 2026. https://we-calculate.com/calculator/y-intercept-calculator.
TG we-Calculate Editorial Team, "Y-Intercept Calculator — Find b in y = mx + b," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/y-intercept-calculator
@misc{wecalculate_y_intercept_calculator, title = {Y-Intercept Calculator — Find b in y = mx + b}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/y-intercept-calculator}}, year = {2026}, note = {TG we-Calculate} }
Did this calculator help you?