Question A curve with polar equation $r = \frac{5}{9 \sin \theta + 7 \cos \theta}$ represents a line. Find the Cartesian equation of the line in the form $y = mx + b$. Select the correct answer below: $y = -\frac{5}{9}x + \frac{7}{9}$ $y = -\frac{7}{9}x + \frac{5}{9}$ $y = \frac{5}{9}x - \frac{7}{9}$ $y = \frac{7}{9}x - \frac{5}{9}$ $y = \frac{5}{7}x - \frac{9}{7}$ $y = -\frac{5}{7}x + \frac{9}{7}$
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We need to convert this to a Cartesian equation in the form $y = mx + b$. Step 2: Recall the relationships between polar and Cartesian coordinates: $x = r \cos \theta$ $y = r \sin \theta$ Step 3: Multiply both sides of the polar equation by the denominator: $r Show more…
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