To adjust the equation \( y = 4x + 1 \) so that it can clear the stars in the Marble slide, you have two primary options: you can alter the slope (the coefficient of \( x \)) or the y-intercept (the constant term).
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Adjusting the Slope: The slope determines how steep the line is. If the slope is too steep (like 4), you might want to lower it to make the line less steep. For example, changing the slope to 2 would give you the equation \( y = 2x + 1 \).
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Adjusting the Y-Intercept: The y-intercept determines where the line crosses the y-axis. If the line needs to be higher or lower to clear the stars, you can modify the y-intercept. For instance, if you change the y-intercept to 4, the equation becomes \( y = 4x + 4 \).
You could also modify both values to find the right balance needed to clear the stars.
For example, if we change the slope to 2 and the y-intercept to 4, the new equation would be:
\[ y = 2x + 4 \]
This gives you different options to achieve the desired outcome for clearing the stars. Let me know if you have a specific scenario in mind, and I can help fine-tune it!