IS item is your proportionate share of the firms Net income. If you own 40%, you report 40% of their net income in your IS.
BS item is usually called “Investment in Associate”, and is considered a LT asset. If you purchase 40% of a firm with cash, for instance, for $1mm
Cash goes down by $1mm, “Investment in Associate” goes up by $1mm
At the next reporting date, say the next year, the firm you invested in reports $100k of net income. You own 40%, so would report $40k in Net income on your IS.
The value of your investment is on the BS at $1mm the net income you report raises the value of the investment by 40k to make it 1,040,000. . The offset is in Shareholders Equity for 40k.
If the firm you invested in reports dividends, the accounting is a little different. The dividends you report are treated as a return of capital. So, with 100k of net income and 60k in dividends, you still report 40k in net income. However, the value of the investment will be reduced. INvestment in associate goes up by the 40k of net income but is reduced by 40% * 60k in dividends (24k). End result is a net increase in the investment of 16k. Cash goes up by 24k in dividends, assets still go up by 40k total. Equity still goes up by 40k.