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