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Quincy is starting a new exercise program. On the first day, he does $10$ push-ups. On the third day, he does $20$ push-ups. On the sixth day, he does $35$ push-ups. Is the relationship between the day and the number of push-ups a linear relationship?$\newline$Choices:$\newline$(A)yes$\newline$(B)no$\newline$Now, justify your answer.$\newline$Choices:$\newline$(A)There is not a clear relationship between the day and the number of pushups.$\newline$(B)The number of push-ups increased at a rate of $10$ push-ups per day.$\newline$(C)The number of push-ups increased by a different amount each day.$\newline$(D)The number of push-ups increased at a rate of $5$ push-ups per day.