Which of the following shows two points on the line f(x)=x-7

The answer is choice (2) and here's why:

The first point (1,-6) means x = 1 and y = -6. Let's replace x and y with these values (1 and -6) into the equation y = x-7 and we'll get...

y = x-7
y = 1-7 ... replace x with 1
-6 = 1-7 ... replace y with -6
-6 = -6 ... this equation is true
Since the equation is true, this means that (1,-6) is on the line

Do the same for the other point (x,y) = (5,-2) to get...

y = x-7
y = 5-7 ... replace x with 5
-2 = 5-7 ... replace y with -2
-2 = -2 ... this equation is true
Since the equation is true, this means the point (5,-2) is also on the line

This confirms that both points are on the line y = x-7

Once again, the answer is choice (2).