Question 24418
The slope form of the equation of the line is given by 
(y-y1) = m(x-x1) where m is the slope and (x1,y1) is the point through which the line passes
So now we have
(y - 5) = 7(x-(-2))
(y-5)= 7(x+2)
y-5 = 7x+14
Taking y-5 to the other side
7x+14 -(y-5)=0
7x+14 -y +5 = 0
 
7x-y +19 = 0

Check:
This line should pass through (-2,5)
7(-2) -5 +19 = 0
-14 +14 = 0
0 =0 Since the Left Hand Side is Equal to the Right hand Side, it means this line passes through (-2,5)