Perpendicular line for 7 x + 5 y equals -1

7x + 5y = -1 
get: y = mx + c
firstly, subtract 7x from both sides:
5y = -7x -1
divide both sides by 5:
y = (-7x -1)/5:
y= -7x/5 -1/5
therefore the slope, m  = -7/5 in the formula y = mx + c
perpendicular test m1 .m2 = -1
m1 = -7/5, substitute in formula:
(-7/5) x m2 = -1
m2 = -1 /(-7/5) which equals [ invert and multiply] -1 x -5/7 = 5/7
perpendicular slope m2 = 5/7 
new line y=mx +c is:
y = 5/7 x -1/5