The graph displays the relationship between the number of cups and the stack height in centimeters. You are asked to determine how much each additional cup after the first increases the height of the stack.

Solution:

1. To determine the height added by each cup, we need to find the slope of the line in the graph.

   • Slope $m$ of a line is calculated as: $m = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1}$
   • Using the two points marked on the graph:
     $(3, 5.5)$ and $(8, 8)$.

2. Now, apply the slope formula: $m = \frac{8 - 5.5}{8 - 3} = \frac{2.5}{5} = 0.5$

This means that each additional cup adds 0.5 cm to the height of the stack.

Final Answer:

• Each cup after the first adds 0.5 cm to the stack height.

Do you want me to explain the concept of slope further or explore more details?
Here are 5 related questions to deepen your understanding:

1. How does changing the slope affect the steepness of the line?
2. If the stack starts with 2 cups, what would be the total height?
3. What would the equation of this line be in slope-intercept form?
4. How can you interpret the y-intercept in this situation?
5. How does the slope help in predicting future values for larger stacks?

Tip: The slope of a graph helps reveal patterns or how one variable changes relative to another. Keep practicing with different graphs to master the concept!