Final answer:
The equation in slope-intercept form that models the total amount paid for fabric with a $5-off coupon is y = 5.50x - 5, where the slope is 5.50 (cost per yard) and the y-intercept is -5 (the coupon discount).
Step-by-step explanation:
You want to write an equation in slope-intercept form for the total amount of money, y, you pay if you buy x yards of fabric with a $5-off coupon. Without the coupon, each yard of fabric costs $5.50, so if you bought x yards, it would normally cost $5.50 times x yards. However, with the coupon, you get a $5.00 discount from the total purchase. Therefore, your equation would subtract $5.00 from the total cost of x yards of fabric at $5.50 per yard.
The equation modeling this situation is:
y = 5.50x - 5
Here, the slope is 5.50, which represents the cost per yard of fabric, and the y-intercept is -5, which represents the $5 discount applied to the purchase.