Question 701518
If you know the {{{highlight(slope)}}}, m, and the coordinates of a {{{highlight(point)}}}, (a,b),
the equation of the line can be written as
{{{y-b=m(x-a)}}}
That is called the {{{highlight(point)}}}-{{{highlight(slope)}}} form of the equation of the line.
It is derived from the definition of {{{highlight(slope)}}} 
as the difference in y-coordinates divided by
difference in x-coordinates for any pair of points on the line.
For any unknown point (x,y) and a known point (a,b),
their coordinates and the slope, m, are related by
{{{(y-b)/(x-a)=m}}} --> {{{y-b=m(x-a)}}}
 
For your problem,
{{{y-(-40)=(4/5)(x-21)}}} --> {{{highlight(y+40=(4/5)(x-21))}}}
That is one of the infinite number of equivalent equations for the line.
It can be transformed into the unique slope-intercept form of the equation for the line.
{{{y+40=(4/5)(x-21)}}} --> {{{y+40=(4/5)x-21(4/5)}}} --> {{{y+40=(4/5)x-84/5}}} --> {{{y=(4/5)x-84/5-40}}} --> {{{y=(4/5)x-84/5-200/5}}} --> {{{highlight(y=(4/5)x-284/5)}}} (in slope-intercept form)