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

Question

y= 1/2 x 0 + 1

Answer 1

It looks like your current equation is incorrectly written as \( y = \frac{1}{2} x \cdot 0 + 1 \), which simplifies to \( y = 1 \). For clarification, I will assume you meant:

\[ y = \frac{1}{2}x + 1 \]

In this equation, the slope is \( \frac{1}{2} \) and the y-intercept is \( 1 \). To adjust the slope or y-intercept so that the marble clears the star, you can either increase the slope (to make the line steeper) or change the y-intercept (to raise or lower the starting point).

Here are some changes you could make:

1. Increase the Slope:

   • Change the slope from \( \frac{1}{2} \) to \( 1 \): \[ y = 1x + 1 \] (This makes the line steeper.)

2. Change the Y-Intercept:

   • Increase the y-intercept from \( 1 \) to \( 2 \) (keep slope the same): \[ y = \frac{1}{2}x + 2 \]

3. Combine Both:

   • Increase the slope to \( 1 \) and change the y-intercept to \( 2 \): \[ y = 1x + 2 \]

Choose the change that fits best with the marble's current trajectory and the position of the star!