What is the slope of a this perpendicular line 0=-15-7x+3y? Explain?

Put it into slope intercept form y=mx+b where m is slope

0=-15-7x+3y

subtract 3y from both sides

-3y=-7x-15

multiply both sides by - 1

3y=7x+15

divide both sdies by 3

y=7/3x+5

slope is 7/3

to find a line perpendicular to it, the slope of the other line, when multiplied by this line, must equal - 1, exg

1/2 and - 2/1 are perpenicular

-1 and 1 are perpendicular

therefor the line perpendicular to it has a slope of - 3/7, exg y=-3/7+3