Bella is paid $35 for selling tickets at Henderson High School football games plus $1 for each program that she sells. Arun is paid $25 for selling tickets at Middletown High School football games plus $1 for each program that he sells. Bella sold 40 programs and Arun sold 65 programs at Saturday’s game. Which of the following correctly compares these additive linear relationships?
The total amount earned by Bella is given by the equation Y = 35 + X, where Y represents the total amount earned and X represents the number of programs sold.
Similarly, the total amount earned by Arun is given by the equation Y = 25 + X.
To compare these linear relationships, we can compare the slopes and the y-intercepts.
The slope of Bella's relationship is 1 because for every program sold, she earns $1. The y-intercept is 35 because even if she doesn't sell any programs, she still earns a flat rate of $35.
The slope of Arun's relationship is also 1 because for every program sold, he earns $1. The y-intercept is 25 because even if he doesn't sell any programs, he still earns a flat rate of $25.
Therefore, the additive linear relationships for Bella and Arun are the same since they both have a slope of 1 and different y-intercepts.