Solve for $y$.
$\frac{y}{-3}=-4$
To solve for \(y\) in the given equation \(\frac{y}{-3} = -4\), we first identify the operation being performed on the variable \(y\). The variable \(y\) is divided by \(-3\). To isolate \(y\), we must perform the inverse operation, which is multiplication. By multiplying both sides of the equation by \(-3\), we can solve for \(y\).
We multiply both sides of the equation \(\frac{y}{-3} = -4\) by \(-3\):
\[\left(\frac{y}{-3}\right) \times (-3) = (-4) \times (-3)\]
Simplifying the left side, \(\frac{y}{-3} \times (-3) = y\).
Calculating the right side, \((-4) \times (-3) = 12\).
Thus, we find that \(y = 12\).
After performing the multiplication, we have found the value of \(y\) to be \(12\). We can verify this by plugging \(12\) back into the original equation: \(\frac{12}{-3} = -4\), which is correct. Therefore, the value of \(y\) is \(\boxed{12}\).
In many real-world scenarios, such as budgeting or science, you often need to reverse an operation to find an unknown value. For example, if you know that a temperature dropped by 3 degrees every hour for a certain number of hours, resulting in a total drop of 12 degrees, you would use this same mathematical principle to find the number of hours passed. Solving equations like this helps us understand relationships between quantities and find unknowns efficiently.