book Maths Puzzle Numerical Ability

A general equation of the family of lines perpendicular to 2x-5y=7 is...

THE ANSWER IS: 5x+2y=k (BUT HOW DO U GET THIS?) please tell me how and why this is the answer

YOUR HELP IS MOST APPRECIATED, THANK YOU SO MUCH

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book Other Question

A local department store sells carpets in 3 sizes. Each carpet comes in 2 different qualities. One of the sizes comes in 6 colors. The other sizes come in 2 colors. How many choices of carpet are there? At a local high school, the ratio of boys to girls is 3:4. there are 1200 boys in the school. how many girls are there?