Question

Find the equation of a line parallel to 5x +6y = 0 at distance sqrt 61 from (-3,7)

I need help please. I don't have any idea

Answer 1

y = -(5/6)x for the first line, so the slope of your second (parallel) line is also -5/6. Its equation is
y' = -(5/6)x + C
C is the y-intercept of the second line.

You have to choose C so that y and y' are sqrt61 apart.

C is the hypotenuse of a right triangle with sides sqrt61 and (5/6)*sqrt61. Its value is sqrt[61 + (25/36)*61]
= sqrt[(61/36)*61] = 61/6

The line you want is
y' = (-5/6)x + 61/6

Answer 2

There is a second line that is also a solution, below the first line
y' = (-5/6)x - 61/6