uppose that \( y \) varies inversely with \( x \), and \( y=2 \) when \( x=10 \). (a) Write an inverse variation equation that relates \( x \) and \( y \). Equation: (b) Find \( y \) when \( x=-4 \) \( y=\square \)
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To express the relationship of inverse variation, we start with the formula \( y = \frac{k}{x} \), where \( k \) is a constant. Given that \( y = 2 \) when \( x = 10 \), we can find \( k \) by substituting these values into the equation: \[ 2 = \frac{k}{10} \] Multiplying both sides by 10 gives us \( k = 20 \). Therefore, the inverse variation equation is: \[ y = \frac{20}{x} \] Now, to find \( y \) when \( x = -4 \), we substitute -4 into the equation: \[ y = \frac{20}{-4} = -5 \] So, \( y = -5 \).