find the point on the line -6x+7y-5=0 which is closest to the point (1,3)

Question

anonymous · Answer

the closest point between a line and a piont lies on a perpendicular line that connect the point and the line 

so for the line we should find the slope 

-4x + 7 y + 6 =0 solve for y 
7y = 4x -6 
y = 4/7 x - 6/7 

so slope is m1= 4/7 

now perpendicular lines have slopes that are negative reciprocals so 
m1= -1/m2 
so 4/7 = - 1/ m2 
m2= -7/4 

now we have a slope m=-7/4 and a point (-5, 1) use slope point formula 

y-y, = m(x-x,) 
y- 1 = -7/4 (x+5) 
y-1 = -7/4 x - 35/4 
y = -7/4 x - 35/4 +1 
y= -7/4 X - 35/4 + 4/4 

Y = -7/4 X - 31/4

anonymous · Answer

please give medal, if helped

anonymous · Answer

but what is the point?

anonymous · Answer

last answer on bottom

anonymous · Answer

I put that it but its asking me for a point not an equation

anonymous · Answer

Refer to the solution and plot from Mathematica 9, that is attached.