Solving ratio problems with graph

In a recent gum-chewing contest, Violet tried to blow the biggest blueberry-flavored bubble ever. Every 3 seconds, she added 1 piece of gum to her huge bubble. On the graph below, the x-axis represents time in seconds. So this right over here is our x-axis. And the y-axis represents pieces of gum in Violet's bubble. So this is the y-axis right over here. Plot points to show how many pieces of gum were in Violet's bubble after 3, 6, and 9 seconds. So every 3 seconds, she adds one piece of gum. So let me throw all of my-- so what we care is about 3 seconds, 6 seconds, and 9 seconds. So every 3 seconds, we know that she adds one piece of gum. This is 0 right over here. We're not going to worry about negative time. So after 3 seconds, she would have added one piece of gum to her bubble. Now, if 3 more seconds pass by, she would have added 1 more, and now she would have 2 pieces of gum in her bubble. And then if 3 more seconds pass by, now we're at 9 seconds, she would have added 1 more piece of gum, and now we're at 3 total pieces of gum. And notice, the ratio between the pieces of gum and the time that has passed has stayed constant, because she's doing it at a constant rate. 1 to 3 is the same ratio as 2 to 6, which is the same ratio as 3 to 9. So, let's check our answer. Very good.