Change the slope or y-intercept value in the equation below to fix the Marble slide so we can clear the star

Answer 1

To adjust the slope or y-intercept of a linear equation to ensure a marble slide clears a star, you need to understand the impact of these values:

1. Slope (m): This determines how steep the line is. Increasing the slope means the line rises more quickly, while decreasing it makes the slide less steep.
2. Y-intercept (b): This is the point where the line crosses the y-axis. Adjusting the y-intercept moves the line up or down without changing its slope.

Example Scenario

If you have an equation of the line given by:

\[ y = mx + b \]

To clear a star situated at a point (x, y):

1. If the marble is falling short of the star (the line is below the star):

   • Increase the y-intercept \( b \) to lift the entire slide up.
   • Increase the slope \( m \) to make the slide steeper, which might also help hit the target higher.

2. If the marble is overshooting the star (the line is above the star):

   • Decrease the y-intercept \( b \) to lower the entire slide.
   • Decrease the slope \( m \) to make the slide less steep, which will help in hitting lower targets.

Steps to Adjust

1. Identify the current values of \( m \) and \( b \).
2. Determine the current trajectory and position of the star.
3. Decide on the necessary adjustments based on the above criteria.
4. Rewrite the equation with the new slope and/or y-intercept.

If you provide the specific equation or details about the marble slide and the star's position, I can give you a more precise adjustment!