Real Life Linear Equations

Summary

In this educational video, the presenter guides viewers through creating real-life linear equations using the DESK method: Define variables, Equation, Solve, and Complete sentence. The focus is on understanding the slope-intercept form (y = mx + b), where 'm' represents the rate of change and 'b' is the starting value. Practical examples, such as saving for retirement and building a book collection, illustrate how to translate word problems into equations and solve for the dependent variable. The video emphasizes the importance of defining variables, setting up equations based on given rates and initial amounts, and solving for specific scenarios, ultimately writing the solution in a complete sentence.

Takeaways

• 📚 The lesson focuses on creating real-life linear equations, particularly using the slope-intercept form (y = mx + b).
• 🔑 The acronym 'DE-SK' is introduced as a method to approach word problems: Define variables, Equation, Solve, and Complete sentence.
• 📈 'D' in DE-SK stands for 'Define', where variables like x (independent) and y (dependent) are assigned to represent different aspects of the problem.
• 📉 'E' in DE-SK stands for 'Equation', where a linear equation is formulated based on the defined variables and the given problem conditions.
• 🔍 'S' in DE-SK stands for 'Solve', which involves substituting the values into the equation to find the solution to the problem.
• ✍️ 'C' in DE-SK stands for 'Complete sentence', emphasizing the importance of providing a clear and full answer to the problem.
• 💡 The lesson uses the terms 'each' and 'per' as indicators to multiply values, and 'starting with' or 'initial amount' as indicators for the constant (b) in the equation.
• 💼 An example is given where Miss Ruddy opens a retirement account with an initial $100 and adds $50 each month, illustrating how to apply the DE-SK method.
• 📚 Another example involves Mr. Lam who starts with 12 books and buys 3 new books each week, further demonstrating the process.
• 📈 The lesson concludes with a challenge for the viewer to apply the DE-SK method to a scenario involving Miss Ruddy's Instagram account, where she gains 7 new followers each day.

Q & A

What does the acronym 'DESK' stand for in the context of solving word problems?

'DESK' stands for Define, Equation, Solve, and Complete sentence. It helps guide the process of solving word problems by first defining variables, forming an equation, solving it, and then writing the answer in a complete sentence.

What do the variables X and Y represent in linear equations, according to the transcript?

In linear equations, X is the independent variable, representing something we choose or control, while Y is the dependent variable, representing what we are trying to find, which depends on the value of X.

How is the 'slope' (M) of a linear equation described in the script?

The slope (M) in a linear equation is described as the change in Y over the change in X. In word problems, M represents how much something changes, such as the rate of increase or decrease.

What does the 'constant' (B) represent in linear equations?

The constant (B) represents the starting value or initial amount in a word problem. It remains unchanged and is added to the equation to reflect the beginning point.

How do keywords like 'each' or 'per' help when solving word problems?

Keywords like 'each' or 'per' indicate multiplication in word problems. For example, '20 students per class' suggests multiplying the number of classes by 20.

In the example problem with Ms. Reddy’s retirement account, how is the equation formed?

The equation is formed as Y = 50X + 100. Here, $50 is added each month (50X) and $100 is the starting amount (constant B).

What is the purpose of writing a complete sentence after solving the equation?

Writing a complete sentence provides clarity by answering the question in a real-world context, ensuring that the solution is meaningful and understandable, rather than just giving a numerical result.

What equation represents the number of books Mr. Lam has after several weeks?

The equation representing the number of books Mr. Lam has is Y = 3X + 12, where 3 represents the number of new books added each week and 12 is the initial number of books.

How does the script suggest solving for different values of X, such as 5 weeks or 10 weeks in Mr. Lam’s library example?

To solve for different values of X, you substitute the desired number of weeks (e.g., X = 5 or X = 10) into the equation Y = 3X + 12 and calculate the total number of books accordingly.

What steps are involved in creating an equation to describe the growth of followers on Ms. Reddy’s Instagram account?

The steps include defining X as the number of days, Y as the total number of followers, and then creating the equation Y = 7X + 3, where 7 represents the new followers gained each day and 3 is the initial number of followers.