To find a perpendicular line you first need to see the equation in slope intercept form. To do that you need to solve for y.
2x - 5y = 20 ---> subtract 2x from both sides -5y = -2x + 20 ---> divide by -5 y = 2/5x - 4
Now that you have this, note that a perpendicular line has opposite and reciprocal slope. Since the slope in our equation is 2/5, that means the new line will have -5/2 slope. So we use the point given and the slope to find the y intercept.
y = mx + b -8 = -5/2(7) + b ---> multiply -8 = -35/2 + b ---> add 35/2 to both sides 19/2 = b
Now use our new slope and new y intercept to write the new equation.
