Final answer:
The correct equation to model the total yards of fabric 'y' for 'x' costumes when 634 yards of fabric are used for 3 costumes is y = (634/3)x yards, which corresponds to option a).
Step-by-step explanation:
The student is asking for an equation that models the relationship between the number of elf costumes made ('x') and the total yards of fabric used ('y'). To find this equation, we need to consider that Mrs. Henderson used 634 yards of fabric for 3 identical costumes. This means that each costume requires 634 yards divided by 3.
To create an equation that represents this situation, we would say that for each additional costume made, the fabric will increase by that same amount. So, the equation in its simplest form is y = (634/3)x yards. This is because for each 'x' number of costumes, we would need 'x' times the fabric required for one costume.
The correct answer from the given options is a) y= 634/3 x yards.