1. slope = (n-k)/(m-j) 2. slope = (n-k))/(m-j) 3. P" = (m,n+e-3) 1. The slope of a line is the ratio between the change in y in regard to the change in x. Since we have two known points on the line r, we can simply subtract their respective x and y coordinates and divide. So slope = (n-k)/(m-j) One thing to pay attention to is to do the subtraction IN THE SAME ORDER. The actual order doesn't matter as long as it's the same for both top and bottom. For instance, this is another equation for the slope that's just as valid. slope = (k-n)/(j-m) 2. This is the exact same way. Just subtract the different y coordinates and divide by the difference between the x coordinates. slope=((n+e)-(k+e))/(m-j) Now because of the associative property, we can do some rearrangement of the expression to get slope=(n+e-k-e))/(m-j) and the "e" terms cancel each other, giving slope=(n-k))/(m-j) And you'll see that the slope is the same as for problem #1 above. 3. For this, let's look at the coordinates of point P' P' = (m,n+e) Since we want to move it 3 units down, just subtract 3 from the y coordinate, so P" = (m,n+e-3)