Find an equation of the line that is perpendicular to the graph of 2x+5y=5 and contains the point of intersection of the graphs of y=x+4 and y–2x=5.

2x+5y=5
5y = - 2x + 5
y = - 2/5x + 1 first equation

first gradient,
m1 = - 2/5

to find second gradient,you must follow the formula,
m1 × m2 = - 1
- 2/5 × m2 = - 1
m2 = 5/2

y = 5/2x + c second equation

y intercept,let x = 0

y=0 + 4
y = 4

x intercept,let y = 0

y–2x=5.
0 - 2x = 5
2x = - 5
x = - 5/2

point of intersection = (-5/2,4)

substitude the point into the second equation to find c

y = 5/2x + c , (-5/2,4)
4 = 5/2(-5/2) + c
4 = - 25/4 + c
c = 41/4

y = 5/2x + 41/4 equation of the line that is perpendicular to the graph of 2x+5y=5