Glencoe Algebra 2, Chapter 2, 2.3, Section 2.3, Problem 50

The purple line has the equation: 2x + 5y = 10 The orange line has the equation that we were asked to find out. It is clearly perpendicular to the purple line and passes through the y-intercept.
This is how I found it out:
Rearranging given equation to make y the subject gives:
y = (-2/5)x + 2
So, the gradient of the line is -2/5 and of the perpendicular is 5/2 (negative reciprocal rule).
We also know a coordinate on the perpendicular: (0, 2)
So, forming it's equation by y - y_(1) = m (x - x_(1))
We can say: y - 2 = 5/2 (x-0)
=> y = (5/2)x +2
This is the required equation and the answer to the question. Thanks!