Slope-Intercept Form Calculator

Slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept (the y-value where the line crosses the y-axis). For example, y = 2x + 3 has a slope of 2 and crosses the y-axis at (0, 3). Any non-vertical line can be written this way.

First calculate the slope: m = (y2 - y1) / (x2 - x1). Then find the y-intercept using b = y1 - m * x1 with either point. For example, from (1, 5) and (3, 11): m = (11 - 5) / (3 - 1) = 3, then b = 5 - 3 * 1 = 2, giving y = 3x + 2.

Plug the slope m and the point (x1, y1) into b = y1 - m * x1. That gives you the y-intercept, and the equation is y = mx + b. The calculator also outputs the point-slope form y - y1 = m(x - x1), which uses the same inputs without an intermediate step.

If both points share the same x-value, the slope is undefined and y = mx + b cannot represent the line. The calculator returns x = c, where c is that shared x-value, the only correct form for a vertical line.

Standard form is Ax + By = C with integer coefficients and A > 0. Starting from y = mx + b, rearrange to mx - y = -b. If m is a fraction, multiply every term by the denominator to clear it, then divide through by the GCD of all three coefficients to reduce to lowest terms. The calculator handles this automatically.