Question

Change the slope or y-intercept value in the equation below to fix the Marbleslide so we can clear the stars.
y=1/2x+1

Answer 1

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.

1. **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:
\[
y = 1x + 1 \quad \text{(or simply)} \quad y = x + 1
\]

2. **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!