How this calculator works
Point-slope form keeps a known point visible in the equation. Subtracting its coordinates from another point gives rise and run measured from that anchor. Multiplying the run by the slope predicts the rise. Expanding the brackets gives y=mx+b with b=y1-mx1. The anchor can be any point on the line; it does not have to be an intercept. This representation uses a finite slope and therefore cannot describe a vertical line.
Formula
y-y1 = m(x-x1); b=y1-mx1; y=y1+m(x-x1); x=x1+(y-y1)/m when m is nonzero.
Worked example
The point (1,3) and slope 2 give y-3=2(x-1). At x=4, the run from the anchor is 3 and the rise is 6, so y=9. Expanding the equation gives y=2x+1.
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Frequently asked questions
Can I choose a different anchor?
Yes. Any point on the same line produces an equivalent equation with the same slope.
Why keep brackets around negative coordinates?
Subtracting a negative coordinate adds its magnitude. Parentheses make the sign explicit and avoid confusing it with the sign of the slope.
What if the slope is zero?
The line is y=y1. Evaluating y is valid, but y alone cannot identify a unique x.
Is a graph included?
The tool returns the equations and requested values. The current engine does not render a line chart.