Given the equation $-26=\frac{y}{13}$, solve for $y$.
The problem requires us to solve for the variable \(y\) in the equation:
\[-26 = \frac{y}{13}\]
To find the value of \(y\), we need to isolate it on one side of the equation. Currently, \(y\) is divided by 13. To reverse this division, we use the inverse operation, which is multiplication.
To isolate \(y\), we multiply both sides of the equation by 13:
\[-26 \times 13 = \left(\frac{y}{13}\right) \times 13\]
On the right side, the multiplication by 13 and the division by 13 cancel each other out, leaving us with:
\[-26 \times 13 = y\]
Now, we calculate the product of \(-26\) and \(13\). Multiplying \(26\) by \(13\) gives \(338\), and since one factor is negative and the other is positive, the result is negative:
\[y = -338\]
We have found that \(y = -338\). Comparing this result with the provided options, it corresponds to the third option. Thus, the correct value for \(y\) is \(\boxed{-338}\).
In financial analysis, if a company's total annual debt change is represented by an average monthly change of \(-26\) units, and the total debt change is \(\frac{y}{13}\) (where \(y\) is the total over 13 months), you can find the total accumulated debt change by multiplying the average monthly change by the number of months. In this case, \(-26 \times 13 = -338\), showing an overall decrease in debt by 338 units over that period. This simple linear relationship is foundational for scaling rates to totals.