Question 888036
Write an equation in slope-intercept form for the line that passes through (h,k) and (u,v).


Slope-intercept form is <b>y=mx+b</b>, using m for slope and b for y-intercept.


{{{highlight_green(m=(v-k)/(u-h))}}}


Solving the basic equation for b,
{{{b=y-mx}}}
and picking either given point, here arbitrarily choosing (h,k) you can find b:
{{{b=k-mh}}}
{{{b=k-((v-k)/(u-h))h}}}
and you might like to simplify the expression (or number) b:
{{{b=(k(u-h)-h(v-k))/(u-h)}}}
{{{b=(ku-hk-hv+hk)/(u-h)}}}, notice the additive inverses hk and -hk,
{{{highlight_green(b=(ku-hv)/(u-h))}}}


Revising the slope-intercept form generalized equation for the two given points,
{{{highlight(y=((v-k)/(u-h))x+(ku-hv)/(u-h))}}}


Note that the process may seem less involved when using actual coordinate values; but not always.  At least with this demonstration, nothing is hidden, and this is generalized.