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