To find the slope, find how much y changes in proportion to x. Here, when x changes by 1, y changes by -2/3. So, the number before x is -2/3.
To find the y-intercept, we need to find what y will be when x is 0. Since we know that when x is 1, y is 16/3, and when x decreases by 1, y increases by 2/3. So, when x is 0, y is 16/3 + 2/3, which is 18/3, or 6.
Let be a sequence that converges to . This means for any , there is some such that for all . From this inequality we see that , so it follows that .
On the other hand, let be a sequence that converges to 0. This means for all large enough , and we get the simpler inequality for free, , so it follows that .