Find the point on the line 7x+1y−2=0 which is closest to the point (−1,−3).
draw a line perpendicular to the first one
what is its slope?
original line:
y = -7 x + 2 so the original slope is -7
slope of perpendicular = -1/-7 = 1/7
now make that perpendicular go through (-1,-3)
-3 = (1/7)(-1) + b
-3 +1/7 = b
b = -20/7
so our line is
y = (1/7)x -20/7
where does that hit our original line
-7x+2 = (1/7)x -20/7
-49 x + 14 = x -20
50 x = -6
x = -3/25
y = -7(-3/25)+2=21/25+50/25 = 71/25