When using the accounting equation, recording the purchase of equipment for cash would include an increase to the (Cash/Equipment/Supplies) account and a decrease to the (Cash/Equipment/Supplies) account.

Equipment account increases, and cash decreases with same amount

Explanation:

In the case of acquisition of a new equipment, the equipment account is debited (increase) while the cash account is credit with the same amount of money used for the purchase.

Purchase of an equipment is a balance sheet item, which means it is recorded in the balance sheet and not the income statement as it is not an expense.

The asset register must also be updated with the value of the newly acquired item