Final answer:
The equation that represents Lisette's savings as she adds money for a car is y = 20x + 972, where y is the total amount saved and x is the number of weeks.
Step-by-step explanation:
Lisette is saving money to buy a car, and the equation that represents the total amount of money Lisette has saved (y) over time, where x is the number of weeks, is y = 20x + 972. This linear equation is derived from the base amount she already has ($972) and the additional amount she saves every week ($20).
To model this situation, we start with her initial savings of $972. Each week, she adds $20 to her savings, which is a consistent weekly addition. Therefore, for every week that passes, represented as x, $20 is added to the initial amount. This relationship is linear and thus can be represented by a linear equation, where the slope (rate of change) is 20, and the y-intercept (starting value) is 972.