mathematics

The equation of a line given two points needs to be found. Samuel claims that slope-intercept form will generate the equation and Helena claims that point-slope form will find the equation. Who is correct? Explain your reason by describing both forms.

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  1. both will work
    the slope of the line between the two points is (y2-y1)/(x2-x1). So, the point-slope form yields
    y-y1 = (y2-y1)/(x2-x1) (x-x1)
    But that is just the same as
    y = (y2-y1)/(x2-x1) x - (y2-y1)/(x2-x1) x1 + y1

    or,
    y-y1 = m(x-x1)
    is the same as
    y = mx + (y1 - m*x1)
    which is
    y = mx+b where b = y1 - m*x1

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    oobleck

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