Slope-Intercept Form Calculator (y = mx + b)
Find the slope-intercept equation y = mx + b from two points or from a slope and a point.
Returns the slope, y-intercept, x-intercept, and a graph of the line.
What slope-intercept form tells you
Slope-intercept form writes a straight line as y = mx + b. It is the version most people remember from algebra because you can read the line straight off it. The m is the slope: how steep the line is and which way it leans. The b is the y-intercept: the height where the line crosses the vertical axis. Pin down those two numbers and the line is fixed for good.
Building it from two points
Get the slope first. Slope is rise over run, so subtract the y-values and divide by the matching difference of the x-values: m = (y2 - y1) / (x2 - x1). Keep the order consistent or the sign flips. Once m is known, plug either point back into the equation and solve for b, since b = y - m*x. That is the whole method, and the calculator shows each step so you can check it against your own work.
Building it from a slope and one point
When a problem hands you the slope and a single point, you skip the rise-over-run step entirely. Drop the slope and the point into b = y - m*x and the equation falls out.
The cases that break the formula
A vertical line has no slope-intercept form. Its run is zero, division by zero is undefined, and the line is written x = constant instead. A horizontal line is the friendly opposite: the slope is zero, the equation collapses to y = b, and there is no x-intercept because the line never reaches the x-axis.
Reading the answer
A slope of 2 climbs twice as fast as a slope of 1, and a negative slope falls as you move right. The y-intercept is the value of y when x = 0; the x-intercept, found from -b/m, is where y = 0. Students lose the most marks by swapping the two intercepts, so the result panel labels each one and plots the line so you can see both crossings.