In this video the instructor shows how to derive a general equation for a line in PointSlope form. The slope of an equation is the ratio of difference of y coordinates to the difference of x coordinates. In other words, slope is the change of y up on change of x. So you have the basic slope equation m = (y2  y1)/(x2  x1). When you have fractions you can simplify them by multiplying the denominator to the numerator on both sides. So multiply the equation by (x2x1) on both sides. This gives you m(x2  x1) = (y2  y1). This is the general form of a line in point slope form. So the general equation can be also written as (y  y1) = m(x  x1). This video shows you how to write an equation of line in PointSlope form.
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