Final answer:
The textile industry transitioned from homes to factories primarily due to Richard Arkwright's water frame, patented in 1769, which used water power for spinning cotton into thread, facilitating increased production efficiency.
Step-by-step explanation:
The invention that helped move the textile industry from homes to factories during the Industrial Revolution was B. Arkwright's water frame. Richard Arkwright patented the water frame in 1769, which harnessed water power to spin cotton into thread. The installation of the water frame in Arkwright's cotton mill in 1771 represented one of the early steps towards factory-based production. Not only did this innovation enable greater efficiency in processing cotton, but it also set a precedent for housing machinery in dedicated factories, as opposed to the prior practice of conducting manufacturing within homes or in smaller workshops.
The development and implementation of the water frame spurred significant growth in textile production and paved the way for subsequent innovations such as the power loom and the spinning mule, which were later powered by steam engines and contributed to a dramatic rise in productivity within the textile industry.