FUNÇÃO DO 1º GRAU | FÁCIL e RÁPIDO

Summary

This educational video delves into functions of the first degree, explaining the concept through a taxi fare scenario. The instructor uses a real-life example, where a fixed initial fare and an additional charge per kilometer are used to build a linear function. The script guides viewers through the process of formulating the function, solving for the value of the fare given a distance, and vice versa. The teacher emphasizes the importance of understanding the structure of first-degree functions, offering practical examples and encouraging viewers to explore further with a comprehensive e-book and online course.

Takeaways

• 😀 The script explains the concept of a linear function (first-degree function) using a real-life example of a taxi ride.
• 😀 The general formula for a linear function is Y = Ax + B, where 'A' represents the rate per unit of change, and 'B' is a fixed starting value.
• 😀 The taxi ride involves a fixed starting charge of R$ 10 (the 'bandeirada') and an additional charge of R$ 2 per kilometer traveled.
• 😀 The 'x' variable in the formula represents the number of kilometers traveled, and 'Y' represents the total cost of the taxi ride.
• 😀 To determine the cost of a taxi ride for a given distance, substitute the value of 'x' (kilometers) into the formula: Y = 2x + 10.
• 😀 An example calculation is given for a 45-kilometer ride, where the cost is calculated as Y = 2 * 45 + 10 = R$ 100.
• 😀 The script emphasizes the importance of converting units (meters to kilometers) when needed for accurate calculations.
• 😀 The law of formation of the function is demonstrated clearly, using the formula Y = 2x + 10 as the standard equation for this taxi problem.
• 😀 In another example, the script shows how to calculate the number of kilometers traveled when the total cost is provided (e.g., R$ 230).
• 😀 To solve for 'x' when the total cost (Y) is given, rearrange the formula to isolate 'x' and perform algebraic operations, resulting in x = 110 kilometers.
• 😀 The lesson concludes with a reminder that the formula for a linear function is essential for solving real-life problems involving rates, such as the taxi fare example.

Q & A

What is a 'função do primeiro grau' (first-degree function) in mathematics?

A 'função do primeiro grau' is a linear function represented by the formula Y = Ax + B, where 'A' is the coefficient of 'x' (also called the slope) and 'B' is the constant term (also known as the y-intercept).

What does the term 'bandeirada' mean in the context of a taxi fare?

The 'bandeirada' is the fixed initial fare charged when entering a taxi. This amount is the base price, regardless of whether the taxi has started moving or not, and in the example, it is R$ 10.

How is the cost of a taxi ride calculated?

The cost of a taxi ride is calculated based on a fixed initial fee (R$ 10, called 'bandeirada') plus an additional charge per kilometer traveled. In this case, R$ 2 per kilometer.

What is the formula for calculating the total cost of a taxi ride?

The formula for calculating the total cost (V) is V = 2x + 10, where 'x' is the number of kilometers traveled, '2' is the cost per kilometer, and '10' is the fixed initial fee.

How do you convert meters into kilometers in this problem?

To convert meters into kilometers, divide the number of meters by 1000. For example, 45,000 meters equals 45 kilometers.

How do you calculate the fare for a 45-kilometer taxi ride?

Using the formula V = 2x + 10, where x = 45 kilometers, you substitute into the equation: V = 2(45) + 10, which gives V = 90 + 10 = R$ 100.

What does the term 'coeficiente angular' mean in the context of the function?

The 'coeficiente angular' (angular coefficient or slope) refers to the 'A' in the linear function Y = Ax + B. It represents how much the dependent variable (Y) changes for each unit change in the independent variable (x). In this case, the slope is 2, indicating that the fare increases by R$ 2 for every additional kilometer traveled.

What is meant by the 'termo independente' in the equation?

The 'termo independente' (independent term) refers to the constant part of the equation, represented by 'B' in the formula Y = Ax + B. In this case, the independent term is 10, which is the fixed fare (bandeirada) that is charged regardless of the kilometers traveled.

How do you determine the number of kilometers traveled if the total fare is known?

To determine the number of kilometers traveled, substitute the total fare (V) into the formula V = 2x + 10. For example, if the fare is R$ 230, the equation becomes 230 = 2x + 10. Subtract 10 from both sides to get 220 = 2x, then divide both sides by 2 to find x = 110 kilometers.

What is the significance of understanding the structure of a first-degree function in real-world applications like taxi fares?

Understanding the structure of a first-degree function allows us to model and calculate costs based on variables that change in a linear manner, such as taxi fares. It helps to predict total costs based on the distance traveled and determine unknowns (like the distance traveled) when the total cost is known.