Asked by jc
                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.
            
            
        Answers
                    Answered by
            oobleck
            
    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
    
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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