The ordered pairs represent (x,y)
To know what ordered pair is a solution we need to substitute the values of x and y with the ordered pair and if the result is equal we have a solution to the equation
For example
(0,-7)
x=0
y=-7
-7=5(0)-7
-7=0-7
-7=-7
Due the result is equal the ordered pair (0,-7) is a solution of y=5x-7