To adjust the equation of the line \( y = \frac{1}{2}x + 1 \) so that it clears the stars on the Marbleslide, you need to modify either the slope or the y-intercept.
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Adjusting the Slope: If you want the line to be steeper (clear higher stars), you can increase the slope. For example, changing the slope to \( 1 \) would give you: \[ y = 1x + 1 \quad \text{(or simply)} \quad y = x + 1 \]
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Adjusting the Y-Intercept: If you believe the slope is fine but want to raise the entire line vertically so that it clears the stars, you can increase the y-intercept. For instance, changing the y-intercept to \( 3 \): \[ y = \frac{1}{2}x + 3 \]
You could pick any combination of values that will provide a line suitable for clearing the stars according to your needs. If you can specify the positions of the stars, I could help determine more precise adjustments for the slope or intercept!
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