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Point-Slope Form

If you know the slope m of a line and the coordinates ( x 1 , y 1 ) of one point on the line, you can write the equation of the line in point-slope form.

y y 1 = m ( x x 1 )

Example:

Find the equation of a line with slope 1 2 passing through the point ( 3 , 2 ) .

Here, m = 1 2 , x 1 = 3 , and y 1 = 2 , so the equation is:

y 2 = 1 2 ( x ( 3 ) )

or

y 2 = 1 2 ( x + 3 )

Slope-intercept form is a special case of point-slope form, where we use the y -intercept coordinate ( 0 , b ) as our point.