x: number of seconds y: number of meters Which equation shows Marlya's distance from the shore? \[ y=2 x \] Which equation shows Olga's Mariya Olga distance from the shore? \[ x=1.5 y+10 \] \[ y=1.5 x \] \( x=1.5 y \) \[ y=1.5 x+10 \]

To determine the correct equations for Marlya's and Olga's distances from the shore, let's analyze the given information and the provided options. ### Given: - **Variables:** - \( x \): Number of seconds - \( y \): Number of meters ### 1. **Marlya's Distance from the Shore** The equation provided for Marlya is: \[ y = 2x \] **Interpretation:** This means that Marlya moves away from the shore at a constant speed of 2 meters per second. ### 2. **Olga's Distance from the Shore** We need to choose the correct equation that represents Olga's distance from the shore. The options provided are: 1. \[ x = 1.5y + 10 \] 2. \[ y = 1.5x \] 3. \[ x = 1.5y \] 4. \[ y = 1.5x + 10 \] **Analysis of Options:** - **Option 1 (\(x = 1.5y + 10\)) and Option 3 (\(x = 1.5y\))**: - These equations express \(x\) in terms of \(y\), which is less conventional for representing distance over time. Typically, distance (\(y\)) is expressed as a function of time (\(x\)). - **Option 2 (\(y = 1.5x\))**: - This equation suggests Olga moves at 1.5 meters per second, similar to Marlya but at a slower speed. However, it doesn't account for any initial distance difference between them. - **Option 4 (\(y = 1.5x + 10\))**: - This equation indicates Olga moves at 1.5 meters per second **and** starts 10 meters ahead of (or behind) the shore. The "+10" represents an initial distance offset. **Conclusion:** **Option 4 (\(y = 1.5x + 10\))** is the most comprehensive and appropriate equation, as it accounts for both Olga's speed and an initial distance from the shore. ### **Final Equations:** - **Marlya:** \[ y = 2x \] - **Olga:** \[ y = 1.5x + 10 \] These equations accurately represent the distances of Marlya and Olga from the shore over time.