Graphing Equations: Unveiling the Relationship Between Variables
Lesson Description
Video Resource
Dependent and independent variables exercise: express the graph as an equation | Khan Academy
Khan Academy
Key Concepts
- Independent variable (t)
- Dependent variable (d)
- Proportional relationships (y = kx)
- Constant of proportionality (k)
- Graph-to-equation translation
Learning Objectives
- Students will be able to identify the independent and dependent variables in a given scenario.
- Students will be able to translate a graph representing a proportional relationship into an equation.
- Students will be able to determine the constant of proportionality from a graph or table.
- Students will be able to explain the meaning of the equation in the context of a real-world situation.
Educator Instructions
- Introduction (5 mins)
Begin by reviewing the concepts of independent and dependent variables. Ask students for examples of situations where one variable depends on another. Briefly discuss proportional relationships and how they can be represented graphically. - Video Viewing (7 mins)
Play the Khan Academy video "Dependent and independent variables exercise: express the graph as an equation". Encourage students to take notes on the key points and example problem. - Guided Practice (10 mins)
Work through the example problem from the video step-by-step on the board. Emphasize the process of identifying the independent and dependent variables, finding the constant of proportionality from the graph or table, and writing the equation. Ask guiding questions to ensure understanding. - Independent Practice (10 mins)
Provide students with additional graph-to-equation problems. Have them work individually or in pairs to solve the problems. Circulate to provide assistance as needed. - Wrap-up & Discussion (3 mins)
Review the answers to the independent practice problems. Discuss any common errors or misconceptions. Reiterate the importance of understanding the relationship between variables and how it can be represented graphically and algebraically.
Interactive Exercises
- Graphing Game
Use an online graphing tool (e.g., Desmos) to graph equations and observe how changing the constant of proportionality affects the graph. - Real-World Scenario Matching
Provide students with a set of graphs and a set of real-world scenarios. Have them match each graph to the scenario it represents and write the corresponding equation.
Discussion Questions
- What is the difference between an independent and a dependent variable?
- How can you identify a proportional relationship from a graph?
- How do you find the constant of proportionality from a graph or table?
- How can you write an equation to represent a proportional relationship?
- How can understanding the equation help you interpret the real-world situation?
Skills Developed
- Identifying independent and dependent variables
- Translating between graphical, tabular, and algebraic representations
- Proportional reasoning
- Problem-solving
- Analytical skills
Multiple Choice Questions
Question 1:
In the equation y = 5x, which variable is the independent variable?
Correct Answer: x
Question 2:
Which of the following equations represents a proportional relationship?
Correct Answer: y = 3x
Question 3:
If a graph shows a straight line passing through the origin, what does it indicate?
Correct Answer: A proportional relationship
Question 4:
What is the constant of proportionality in the equation y = 8x?
Correct Answer: 8
Question 5:
In a graph of hours worked (x) vs. money earned (y), which is the dependent variable?
Correct Answer: Money earned
Question 6:
If you buy apples at $2 per apple, the equation is y=2x. What does 'y' represent?
Correct Answer: Total cost
Question 7:
Which of these is NOT needed to write an equation from a graph?
Correct Answer: Favorite color
Question 8:
What is the first step when converting a graph into an equation?
Correct Answer: Identify the variables
Question 9:
If a job pays $15 an hour, what is the constant of proportionality?
Correct Answer: 15
Question 10:
The equation y=kx represents what type of relationship?
Correct Answer: Proportional
Fill in the Blank Questions
Question 1:
The variable that is changed in an experiment is called the __________ variable.
Correct Answer: independent
Question 2:
The variable that is measured in an experiment is called the __________ variable.
Correct Answer: dependent
Question 3:
In the equation y = kx, 'k' represents the __________ of proportionality.
Correct Answer: constant
Question 4:
A graph that shows a straight line through the origin represents a __________ relationship.
Correct Answer: proportional
Question 5:
The equation d = 65t represents the distance (d) traveled at a speed of 65 mph for time (t). In this equation, 65 is the ___________.
Correct Answer: constant
Question 6:
If y = 7x, then when x is 3, y is ___________.
Correct Answer: 21
Question 7:
When graphing, the independent variable is usually put on the ___________ axis.
Correct Answer: x
Question 8:
When graphing, the dependent variable is usually put on the ___________ axis.
Correct Answer: y
Question 9:
A proportional relationship can also be called a ___________ variation.
Correct Answer: direct
Question 10:
In the equation y = kx, if k is 0, then y will always be ___________ no matter what x is.
Correct Answer: zero
Educational Standards
Teaching Materials
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