Final answer:
To enlarge the photo from 2 inches by 3 inches to 3 inches by 4.5 inches, the scale factor is calculated by dividing the new width by the original width, yielding a scale factor of 1.5.
Step-by-step explanation:
Matt would like to enlarge his photo from a 2-inch by 3-inch size to a 3-inch by 4.5-inch size, and we need to determine the scale factor for this enlargement. To figure out the scale factor, you can compare the sizes of corresponding sides of the two photos. Using either the length or the width to calculate the factor will work, as long as you use the same sides in both photos. In this case, we can use the width to calculate the scale factor since it's simpler (2 inches to 3 inches rather than 3 inches to 4.5 inches).
Divide the new width by the original width to determine the scale factor:
3 inches (new width) ÷ 2 inches (original width) = 1.5.
So, the scale factor that Matt will use to enlarge the photo is 1.5.