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Point-slope formula Point-Slope Formula

Point-slope formula

Use this when you know a slope and one point on the line.

Main form
y − y1 = m (x − x1)
(x1, y1) = the point you know
m = the slope

How to use it (quick)

Pick the point (x1, y1) and the slope m.
Plug them into y − y1 = m (x − x1).
Simplify if you want (optional).
Note: a slope like 2 can be written as 2/1 (rise 2, run 1).

Example A

Point (2,3), slope m = 2
y − 3 = 2 (x − 2)
y − 3 = 2x − 4
y = 2x − 1 (optional)
0 1 1 2 2 3 3 4 4 5 5 x y ( 2, 3 ) run 1 rise 2 Example A: m = 2 through (2,3)

Example B

Point (4,4), slope m = −1
y − 4 = −1 (x − 4)
y − 4 = −x + 4
y = −x + 8 (optional)
0 1 1 2 2 3 3 4 4 5 5 x y ( 4, 4 ) run 1 down 1 Example B: m = −1 through (4,4)
Arrow check: moving left → right, the line going up means positive slope. Going down means negative.
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