Given line: 2x + 5y + 7 = 0

So, its slope is given by

5y = -2x – 7

y = (-2/5) – 7/5

⇒ m = -2/5

Now, let the slope of the line perpendicular to this line be m’

Then,

m x m’ = -1

(-2/5) x m’ = -1

⇒ m’ = 5/2

Also given, the y-intercept (c) = -3

Hence, the equation of the line is given by

y = m’x + c

y = (5/2) x + (-3)

2y = 5x – 6

5x – 2y – 6 = 0