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in a recent gum-chewing contest violet tried to blow the biggest blueberry flavored bubble ever every three seconds she added one 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 violets bubbles so this is the y-axis right over here plot points to show how many pieces of gum were in violets bubble after three six and nine seconds so every three seconds she adds one piece of gum so let me throw all my let me let me throw all of my so what we care is about three seconds six seconds and nine seconds so every three seconds we know that she adds one piece of gum so after three seconds this is zero right over here we're not going to worry about negative time so after three seconds she would have added one piece of gum to her bubble now three more seconds passed by she would have had it one more now she would have two pieces of gum in her bubble and then if three more seconds passed by now we're at nine seconds she would have added one more piece of gum and now we're at three 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 one two three is the same ratio as two two six which is the same ratio as three to nine so let's check our answer very good