Question

name date 2-5-26 period 5
cool down
lesson 5: introduction to linear relationships
cool down: stacking more cups
a different style of cup is stacked. the graph shows the height of the stack in centimeters for different numbers of cups. how much does each cup after the first add to the height of the stack? explain your reasoning.
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Explanation:

Step1: Identify two points

We have two points on the line: \((3, 5.5)\) and \((8, 8)\). Let the number of cups be \(x\) and height be \(y\).

Step2: Calculate the slope

The slope \(m\) of a line passing through two points \((x_1,y_1)\) and \((x_2,y_2)\) is given by \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Substituting \(x_1 = 3,y_1=5.5,x_2 = 8,y_2 = 8\), we get \(m=\frac{8 - 5.5}{8 - 3}=\frac{2.5}{5}=0.5\). The slope represents the rate of change of height with respect to the number of cups, which is the height added by each additional cup (after the first).

Answer:

Each cup after the first adds \(0.5\) centimeters (or \(\frac{1}{2}\) centimeter) to the height of the stack.