Problem

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

Solution

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 :\(\boxed{\text{Therefore, the given equation is neither a direct variation nor an inverse variation.}}\)

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