Answer:
The equation y = 75 - 2.85x represents the amount of money left on the gift card, where x is the number of Chai lattes Angie has purchased and y is the remaining gift card balance.
To find the x-intercept, we set y = 0 and solve for x:
0 = 75 - 2.85x
2.85x = 75
x = 26.32 (rounded to the nearest tenth)
So the x-intercept is approximately 26.3 Chai lattes, meaning that Angie can buy a maximum of 26 Chai lattes with her gift card.
To find the y-intercept, we set x = 0 and solve for y:
y = 75 - 2.85(0)
y = 75
So the y-intercept is $75, meaning that when Angie has not yet bought any Chai lattes, her gift card balance is $75.
To predict how many Chai lattes Angie has purchased when her gift card balance is about $35, we set y = 35 and solve for x:
35 = 75 - 2.85x
2.85x = 40
x = 14.04 (rounded to the nearest tenth)
So when Angie's gift card balance is about $35, she has purchased approximately 14 Chai lattes.