Question 742132
The slope of the line connecting (-3,4) and (-2,1) can be calculated as the difference of the y-coordinates divided by the difference of the x coordinates.
Subtracting the coordinates of (-3,4) minus the coordinates of (-2,1), we get
{{{slope=m=(4-1)/(-3-(-2))=3/(-3+2)=3/(-1)=-3}}}
 
The opposite side is parallel, and parallel lines have the same slope, so the line we want also has slope {{{m=-3}}}.
 
The equation of a line with slope {{{-3}}} and passing through point (2,6) can be written in point-slope form as
{{{y-6=-3(x-2)}}}
 
The more traditional (and unique) slope-intercept form of the equation can be derived from the point-slope form above.
{{{y-6=-3(x-2)}}} --> {{{y-6=-3x-3*(-2)}}} --> {{{y-6=-3x+6}}} --> {{{highlight(y=-3x+12)}}}