Graph Proportional Relationships Quick Check...

Answer 1

It seems like you might be looking for assistance with a quick check or review of graphing proportional relationships. Here are some key points and steps to help you understand how to graph proportional relationships:

Key Concepts

1. Proportional Relationships:

   • A relationship is proportional if it can be described by the equation \( y = kx \), where \( k \) is the constant of proportionality.
   • The graph of a proportional relationship is a straight line that passes through the origin (0,0).

2. Finding the Constant of Proportionality:

   • The constant of proportionality \( k \) can be found by dividing \( y \) by \( x \) for any point on the line, where \( k = \frac{y}{x} \).

Steps to Graph Proportional Relationships

1. Create a Table of Values:

   • Select several values for \( x \).
   • Calculate the corresponding \( y \) values using \( y = kx \).

2. Plot the Points:

   • On a coordinate plane, plot the points \((x, y)\) you calculated.

3. Draw the Line:

   • Once the points are plotted, draw a straight line through all of them, extending the line in both directions. The line should pass through the origin.

4. Identify the Constant of Proportionality:

   • If you have the equation already, determine \( k \) and label your graph accordingly.

Example

Suppose the relationship is defined by the equation \( y = 3x \):

1. Create a Table:

   • If \( x = 1 \), then \( y = 3(1) = 3 \) → point (1, 3)
   • If \( x = 2 \), then \( y = 3(2) = 6 \) → point (2, 6)
   • If \( x = 3 \), then \( y = 3(3) = 9 \) → point (3, 9)

2. Plot the Points: (1, 3), (2, 6), (3, 9)

3. Draw the Line: Connect the points with a straight line through the origin.

4. Constant of Proportionality: The constant of proportionality \( k = 3 \).

Practice Problems

• Given the equation \( y = 4x \), plot the points and graph the line.
• Determine the constant of proportionality for the dataset: \( (2, 8), (3, 12), (5, 20) \).

If you have specific questions or need help with a particular problem, feel free to ask!

Answer 2

100% CORRECT ANSWERS to Quick Check are...

1. C (0,0) (2,1) (4,2) Note: order of the answer may change from C
2 3/2, 3
3. Greg
4. D ($3.75, 1 1/2 lbs) Note: order of answer may change from D
5. B (2, $30) Note: order of answer may change from B

Answer 3

It looks like you've provided answers to a Quick Check related to graphing proportional relationships. Here's a breakdown of the answers you've shared:

1. Answer: C - Points (0,0), (2,1), (4,2)

   • This suggests a proportional relationship where the slope might be \( \frac{1}{2} \).

2. Answer: \( \frac{3}{2}, 3 \) - This likely refers to identifying proportionality constants or specific values related to a problem.

3. Answer: Greg - This might refer to a person associated with a particular question or scenario in the Quick Check.

4. Answer: D - Coordinates \((3.75, 1 \frac{1}{2} \text{ lbs})\) indicate a specific point relating to weight or cost, suggesting a proportional relationship in a real-world context.

5. Answer: B - Coordinates \((2, $30)\) likely suggest a transaction point related to cost.

If these answers pertain to a specific set of questions and context, it would be helpful to see those questions so I can better assist you! If you need any further analysis or explanation on a particular question or point, just let me know!