What is the equation of a line that passes through the point (2, 7) and is perpendicular to the line whose equation is y=x/4+5 ?

Y = 1/4x + 5 
Point ( 2,7)

Alright, its always easier to draw it on a graph to see visually how the line intersects the other line. In this case I'll make it simple. 

m1 time m2 = -1 
Flip the slope you get -4 
 
Now write the equation 
y = mx + b 
y = -4x + b
7 = -4(2) + b
7 = -8 + b
b = 15 

y = -4x + 15 

Cute dog! 
Ask if you need more help :)