To adjust the equation \( y = \frac{1}{2}x + 1 \) to "fix the Marble side so we can clear the stars," you would generally want to either change the slope or the y-intercept in a way that achieves your goal.
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Adjusting the Slope: If your goal is to increase the steepness of the line, you could increase the slope. For example, changing the slope from \( \frac{1}{2} \) to \( 1 \) would give you: \[ y = 1x + 1 \quad \text{(or simply } y = x + 1\text{)} \] Alternatively, if you want to decrease the slope, you could change it to \( \frac{1}{4} \): \[ y = \frac{1}{4}x + 1 \]
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Adjusting the Y-Intercept: If you want to move the line up or down, you'd change the y-intercept. For instance, changing \( 1 \) to \( 2 \) would give you: \[ y = \frac{1}{2}x + 2 \] If you decrease the y-intercept to \( 0 \), you would have: \[ y = \frac{1}{2}x + 0 \quad \text{(or simply } y = \frac{1}{2}x\text{)} \]
Choose the adjustment based on the specific requirements or constraints you have regarding "clearing the stars."