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chocolate milk that all taste the same. 4 The relationship is proportional, so we can connect the points on a graph with a straight line that passes through the origin. Let's find the slope of this line. The slope is the change in vertical distance for a given change in horizontal distance. We can use any two points on the line to help us find the slope. Start by finding the change in vertical and horizontal distance from (2, 8) to (10, 40). Amount of milk (oz) 80 72 64 56 48 40 32 24 16 00 0 (2,8) 1 2 3 (10, 40) 4 5 6 7 8 9 10 Amount of syrup (oz) Enter ✔

chocolate milk that all taste the same. 4 The relationship is proportional, so we can connect the points on a graph with a straight line that passes through the origin. Let's find the slope of this line. The slope is the change in vertical distance for a given change in horizontal distance. We can use any two points on the line to help us find the slope. Start by finding the change in vertical and horizontal distance from (2, 8) to (10, 40). Amount of milk (oz) 80 72 64 56 48 40 32 24 16 00 0 (2,8) 1 2 3 (10, 40) 4 5 6 7 8 9 10 Amount of syrup (oz) Enter ✔

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Transcription and Explanation for Educational Website:** **Title: Understanding Proportional Relationships in Chocolate Milk Making** **Description:** Karen makes chocolate milk. The table shows the proportional relationship between the amount of chocolate syrup she uses, \( x \), and the number of ounces of milk she uses, \( y \), for different batches of chocolate milk that all taste the same. **Text Box:** The relationship is proportional, so we can connect the points on a graph with a straight line that passes through the origin. Let’s find the slope of this line. The slope is the change in vertical distance for a given change in horizontal distance. We can use any two points on the line to help us find the slope. Start by finding the change in vertical and horizontal distance from \( (2, 8) \) to \( (10, 40) \). **Graph Explanation:** - **Axes:** - The x-axis represents the amount of chocolate syrup in ounces (oz), ranging from 0 to 10. - The y-axis represents the amount of milk in ounces (oz), ranging from 0 to 80. - **Data Points:** - Two key points are highlighted: \( (2, 8) \) and \( (10, 40) \). - **Line:** - A straight line connecting the points, illustrating the proportional relationship. The line passes through the origin, which confirms proportionality. - **Determining Slope:** - Calculate the slope using the formula: slope \( = \frac{\text{change in y}}{\text{change in x}} \). - From \( (2, 8) \) to \( (10, 40) \), the change in \( x \) is \( 10 - 2 = 8 \). - The change in \( y \) is \( 40 - 8 = 32 \). - Slope \( = \frac{32}{8} = 4 \). The slope tells us that for every ounce of syrup, 4 ounces of milk are used, keeping the taste consistent for different batch sizes.
Transcribed Image Text:**Transcription and Explanation for Educational Website:** **Title: Understanding Proportional Relationships in Chocolate Milk Making** **Description:** Karen makes chocolate milk. The table shows the proportional relationship between the amount of chocolate syrup she uses, \( x \), and the number of ounces of milk she uses, \( y \), for different batches of chocolate milk that all taste the same. **Text Box:** The relationship is proportional, so we can connect the points on a graph with a straight line that passes through the origin. Let’s find the slope of this line. The slope is the change in vertical distance for a given change in horizontal distance. We can use any two points on the line to help us find the slope. Start by finding the change in vertical and horizontal distance from \( (2, 8) \) to \( (10, 40) \). **Graph Explanation:** - **Axes:** - The x-axis represents the amount of chocolate syrup in ounces (oz), ranging from 0 to 10. - The y-axis represents the amount of milk in ounces (oz), ranging from 0 to 80. - **Data Points:** - Two key points are highlighted: \( (2, 8) \) and \( (10, 40) \). - **Line:** - A straight line connecting the points, illustrating the proportional relationship. The line passes through the origin, which confirms proportionality. - **Determining Slope:** - Calculate the slope using the formula: slope \( = \frac{\text{change in y}}{\text{change in x}} \). - From \( (2, 8) \) to \( (10, 40) \), the change in \( x \) is \( 10 - 2 = 8 \). - The change in \( y \) is \( 40 - 8 = 32 \). - Slope \( = \frac{32}{8} = 4 \). The slope tells us that for every ounce of syrup, 4 ounces of milk are used, keeping the taste consistent for different batch sizes.
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