Determine whether the equation presents a case of direct variation, inverse variation, or neither:
\[
-3 x+4 y=-1
\]
Direct variation
Constant of variation: $k=\square$
Inverse variation
Constant of variation: $k=\square$
Neither
Answer
\(\boxed{\text{Therefore, the given equation is neither a direct variation nor an inverse variation.}}\)
Step 1 ：Given the equation \(-3x + 4y = -1\).
Step 2 ：Rearrange the equation to isolate y, resulting in \(4y = 3x - 1\) or \(y = \frac{3}{4}x - \frac{1}{4}\).
Step 3 ：This equation is in the form \(y = mx + b\), which is the standard form of a linear equation, not a direct or inverse variation.
Step 4 ：In direct variation, the equation should be in the form \(y = kx\), with no constant term (b = 0). In inverse variation, the equation should be in the form \(y = k/x\).
Step 5 ：\(\boxed{\text{Therefore, the given equation is neither a direct variation nor an inverse variation.}}\)
