To determine which ordered pairs represent points on the graph of the equation \( x = \frac{3}{5}y \), we can rearrange this equation to express \( y \) in terms of \( x \):
\[ y = \frac{5}{3}x \]
Now we can check each ordered pair (x, y) to see if it satisfies the equation \( x = \frac{3}{5}y \).
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For the point \((-5, 3)\): \[ -5 = \frac{3}{5}(3) \Rightarrow -5 = \frac{9}{5} \quad \text{(False)} \]
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For the point \((-3, -5)\): \[ -3 = \frac{3}{5}(-5) \Rightarrow -3 = -3 \quad \text{(True)} \]
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For the point \((3, 5)\): \[ 3 = \frac{3}{5}(5) \Rightarrow 3 = 3 \quad \text{(True)} \]
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For the point \((-5, -3)\): \[ -5 = \frac{3}{5}(-3) \Rightarrow -5 = -\frac{9}{5} \quad \text{(False)} \]
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For the point \((5, -3)\): \[ 5 = \frac{3}{5}(-3) \Rightarrow 5 = -\frac{9}{5} \quad \text{(False)} \]
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For the point \((3, -5)\): \[ 3 = \frac{3}{5}(-5) \Rightarrow 3 = -3 \quad \text{(False)} \]
The ordered pairs that satisfy the equation \( x = \frac{3}{5}y \) are:
- \((-3, -5)\)
- \((3, 5)\)
So the correct answers are:
- (-3, -5)
- (3, 5)