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.

Answer 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