For inverse variation, we can express the relationship between \(x\) and \(y\) as:
\[ xy = k \]
where \(k\) is a constant. We will first find \(k\) using the given values of \(x\) and \(y\), and then we will use this constant to find \(y\) when \(x = 3\).
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For \(x = 1, y = 9\): \[ k = xy = 1 \cdot 9 = 9 \] The equation is \(xy = 9\).
To find \(y\) when \(x = 3\): \[ 3y = 9 \quad \Rightarrow \quad y = \frac{9}{3} = 3 \] -
For \(x = -3, y = 8\): \[ k = xy = -3 \cdot 8 = -24 \] The equation is \(xy = -24\).
To find \(y\) when \(x = 3\): \[ 3y = -24 \quad \Rightarrow \quad y = \frac{-24}{3} = -8 \] -
For \(x = 7, y = 2\): \[ k = xy = 7 \cdot 2 = 14 \] The equation is \(xy = 14\).
To find \(y\) when \(x = 3\): \[ 3y = 14 \quad \Rightarrow \quad y = \frac{14}{3} \approx 4.67 \] -
For \(x = \frac{3}{4}, y = 28\): \[ k = xy = \frac{3}{4} \cdot 28 = 21 \] The equation is \(xy = 21\).
To find \(y\) when \(x = 3\): \[ 3y = 21 \quad \Rightarrow \quad y = \frac{21}{3} = 7 \] -
For \(x = -4, y = -\frac{5}{4}\): \[ k = xy = -4 \cdot -\frac{5}{4} = 5 \] The equation is \(xy = 5\).
To find \(y\) when \(x = 3\): \[ 3y = 5 \quad \Rightarrow \quad y = \frac{5}{3} \approx 1.67 \] -
For \(x = -12, y = -\frac{1}{6}\): \[ k = xy = -12 \cdot -\frac{1}{6} = 2 \] The equation is \(xy = 2\).
To find \(y\) when \(x = 3\): \[ 3y = 2 \quad \Rightarrow \quad y = \frac{2}{3} \approx 0.67 \]
Summary of results when \(x = 3\):
- \( y = 3 \)
- \( y = -8 \)
- \( y \approx 4.67 \)
- \( y = 7 \)
- \( y \approx 1.67 \)
- \( y \approx 0.67 \)