Find the point on the line 7x+4y-2=0 which is closest to the point (-5,-6).

Find the point on the line 7x+4y-2=0 which is closest to the point (-5,-6).

i get y=(2-7x)/4 and plugged into distance formula:

d=sqrt((x+5)^2+((2-7x)/4+6)^2)

Taking the derivative of this seems like it would be a mess. did i do something wrong?

Square both sides before taking derivative,
d^2 = (x+5)^2+((2-7x)/4+6)^2
Take derivative with respect to x,
2dd' = 2(x+5) + 2((2-7x)/4+6)(-4/7)
Solving d' = 0 gives you the answer.

Can you finish?

1) Convert to slope-intercept form.
4y=-7x-2.
2) Solve for y.
y= -7/4x-1/2 (2/4 reduced)
3) I would graph the point (-5, -6) and then graph the line and find the coordinate closest to (-5, -6)