Find the point on the line 5x+2y−7=0 which is closest to the point (−2−6).

5x + 2y - 7 = 0
2y = - 5x + 7
y = - 5/2x + 7/2
Line perpendicular passing through (- 2,- 6)
Line perpendicular would have slope 2/5
y - y1 = m(x - x1)
y - - 6 = 2/5(x - - 2)
y + 6 = 2/5(x + 2)
y + 6 = 2/5x + 4/5
y = 2/5x + 4/5 - 6
y = 2/5x - 26/5
5y = 2x - 26.....(1) multiply by 5 ... 25y = 10x - 130
2y = - 5x + 7.....(2) multiply by 2....4y = - 10x + 14 Add
29y = - 116
y = - 116 / 29
y = - 4
Sub for y in(1)
5*(-4) = 2x - 26
- 20 = 2x - 26
- 20 + 26 = 2x
6 = 2x
3 = x
(3, - 4)