Enter two points on a line — x1, y1, x2, y2 — and get the slope (m), y-intercept (b), and x-intercept back. The Slope and Intercept Calculator also returns the full slope-intercept equation (y = mx + b), point-slope form, and standard form so you have everything you need in one place.
Slope (m)
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Y-Intercept (b)
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X-Intercept
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Slope-Intercept Form
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Point-Slope Form
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Rise (Δy)
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Run (Δx)
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The slope-intercept form of a linear equation is y = mx + b, where m is the slope of the line and b is the y-intercept (the point where the line crosses the y-axis). It is one of the most common ways to express a straight line because both key parameters — steepness and position — are immediately visible.
Slope (m) is calculated as the change in y divided by the change in x: m = (y2 − y1) / (x2 − x1). This is often called 'rise over run.' A positive slope means the line goes upward left to right, while a negative slope means it goes downward.
Once you have the slope m, substitute one of your known points into y = mx + b and solve for b. For example, if m = 2 and your point is (3, 7): 7 = 2(3) + b, so b = 1. The y-intercept is the value of y when x equals zero.
The x-intercept is the point where the line crosses the x-axis, meaning y = 0. Set the equation to 0 = mx + b and solve: x = −b / m. This tells you at what x-value the line hits the horizontal axis.
No. Slope-intercept form is y = mx + b, while standard form is Ax + By = C. Both describe the same line but are arranged differently. You can convert between them by rearranging the equation algebraically.
A slope of zero means the line is perfectly horizontal — there is no rise for any run. The equation simplifies to y = b, a constant. Conversely, an undefined slope (division by zero when x1 = x2) means the line is perfectly vertical.
Parallel lines have identical slopes (m1 = m2) but different y-intercepts. Perpendicular lines have slopes that are negative reciprocals of each other — that is, m1 × m2 = −1. For example, if one line has slope 2, a perpendicular line has slope −1/2.
Slope and intercept appear in economics (cost functions), physics (velocity), engineering (gradients), and data science. In machine learning, linear regression fits a line y = mx + b to data where m and b are learned parameters that minimize prediction error across many data points.