Line segment wih points as integers

The y-intercept of the line is 30, and the slope is -30/50. So the equation of the line is:

y = -(3/5)x + 30

There are 51 integers we can plug in for x (anything from 0 to 50), but we'll only get an integer value of y if x is a multiple of 5 (otherwise the '5' in the denominator of 3/5 won't cancel). So the values of x that will give us integer co-ordinates are 0, 5, 10, 15 ..., 45, 50 = 0*5, 1*5, 2*5, ..., 9*5, 10*5, or eleven values in total.