How this calculator works
In y=mx+b, m is the change in y per one-unit increase in x and b is the value at x=0. Two points recover m by dividing their rise by their run, then substituting either point gives b. This makes the form useful for a constant rate with an initial amount. The x intercept is -b/m for a nonzero slope. For a horizontal line it is omitted because there is either no crossing or an entire axis of crossings.
Formula
y=mx+b; m=(y2-y1)/(x2-x1); b=y1-mx1; x intercept=-b/m; inclination=atan(m); grade=100m percent.
Worked example
A tank model y=-3x+7 starts at 7 units when x=0 and decreases by 3 units per step. Its x intercept is 7/3. Separately, points (1,3) and (3,7) give m=2 and b=1.
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Frequently asked questions
What does a negative intercept mean?
The line crosses the y axis below the origin. Whether that value is meaningful depends on the model domain.
Why is a vertical line rejected?
One x value would have many possible y values, so it cannot be expressed as a function y=mx+b with finite m.
Does b have the same units as m?
No. The intercept uses y units, while slope uses y units per x unit.
Can I see a graph?
The calculator returns equations, intercepts and numeric properties. A rendered graph is not available on this engine.