Through (4,3), perpendicular to 2x-5y=7

First you want to get it to y=mx+b. to do this you have to get the y by itself on one side. 2x-5y=7 you bring - 5y over and get 2x=5y+7. Then bring the 7 over and get 2x-7=5y and finally get rid of the 5 by dividing both sides by it 2x-7/5 turns into 2/5x-7/5 and 5y becomes y. Y=2/5X-7/5. Next to get the slope of a line perpendicular to another you first flip the original slope (2/5x to 5/2x) and then reverse the sign (5/2x to - 5/2x). and now you have Y=-5/2X+B. To get B you must put in what you know (X is 4, Y is 3) Get 3=-5/2 (4) + B and solve.

3=-5/2 (4) + B to 3=-10+B. bring - 10 over and get 13=B and put that in. Finally you have Y=-5/2X+13.