Question

Solve the equation for the y-value and choose whether it is a direct variation or inverse variation.

-4x+y=0

direct variation

inverse variation

Answer 1

To solve the equation \(-4x + y = 0\) for \(y\), we can isolate \(y\):

1. Add \(4x\) to both sides:
\[
y = 4x
\]

Now we have the equation \(y = 4x\).

### Check for Direct or Inverse Variation

1. **Direct Variation:** A relationship is a direct variation if it can be expressed in the form \(y = kx\) where \(k\) is a constant. In this case, since we have \(y = 4x\), where \(k = 4\), this is a direct variation.

2. **Inverse Variation:** A relationship is an inverse variation if it can be expressed in the form \(y = \frac{k}{x}\) where \(k\) is a constant. The given equation does not match this form.

### Conclusion

The solution for the \(y\)-value is \(y = 4x\), and this represents a **direct variation**.