Final answer:
The slope-intercept form of the equation representing the amount of money Marissa has left on her $25 Roosters on Oxford gift card after buying a $3 vanilla latte for x visits is y = -3x + 25. The y-intercept is the original value of the card, which is $25, and the slope is -3, representing the cost of each latte.
Step-by-step explanation:
To write a linear equation which represents the amount of money Marissa has on her gift card after x visits, we need to recognize two things: how much money she starts with (the y-intercept) and how much money is deducted with each purchase (the slope).
The amount Marissa starts with is the value on the gift card, which is $25. This is our y-intercept, and it will be our starting point when x (the number of visits) is 0. Therefore, when x is 0, y will be 25.
The cost of the vanilla latte each morning is $3. Since this amount is deducted from the card with each visit, our slope will be negative because the balance decreases with each purchase. Therefore, the slope is -3.
Putting these together, the equation in slope-intercept form (which is y = mx + b where m is the slope and b is the y-intercept) would be y = -3x + 25.
This equation means that for every visit x, $3 times the number of visits (3x) is subtracted from the original balance of $25.