Question 538744
{{{4x-7y=28}}}---> {{{7y=4x-28}}}---> {{{y=(4/7)x-4}}} shows the slope of the line is 4.
The perpendicular line has a slope of {{{1/(-4)=-1/4}}}.
The point-slope form of the perpendicular line through (4, -2) written using point (4, -2) and slope -1/4 is
{{{y-(-2)=(-1/4)(x-4)}}} or {{{y=2=-(1/4)x+1}}}
There are as many point-slope forms as points in a line (infinity), but there is only one slope-intercept form of the equation, starting with "y=" and that is:
{{{y=-(1/4)x-1}}}