## Podcast Beta

## Questions and Answers

What is the characteristic of linear equations in terms of the power of variables?

What is the standard form of a linear equation involving two variables x and y?

Which of the following equations is not linear?

What is the characteristic of linear equations in terms of the product of variables?

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What is the general form of a linear equation involving 'n' variables?

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Which of the following equations is linear?

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What is the first step to determine a pair of values that satisfy a linear equation?

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In the equation y = 2x + 500, what is the value of y when x = 20?

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What is the purpose of using linear equations in business application problems?

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In the production problem, how many hours of labor are required to produce one unit of product A?

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What is the total number of hours available for manufacturing products A and B?

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What is the general form of a linear function in business application problems?

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What is the general form of a linear function involving one independent variable x and a dependent variable y?

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What does the slope 'a1' represent in a linear function?

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What is the weekly salary of the salesperson if they sold 150 units in a week, according to the equation y = 3x + 25?

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What is the change in the weekly salary associated with each additional unit sold, according to the equation y = 3x + 25?

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What is the fixed cost of production, according to the equation y = 3x + 25?

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What is the relationship between the change in weekly salary and the change in number of units sold, according to the equation y = 3x + 25?

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## Study Notes

### Linear Equations and their Characteristics

- Linear equations are equations whose terms are constant or a constant times one variable to the first power.
- Characteristics of linear equations:
- Linear equations are first degree equations, where each variable is raised to the first power.
- The presence of terms with exponents other than 1 excludes an equation from being considered linear.
- Linear equations involve a product of a constant term with a variable, but not a product of variables.

- Standard form of a linear equation involving two variables: ax + by = C, where a, b, and C are constants, and a and b cannot both equal zero.

### Solving Linear Equations

- To determine a pair of values that satisfy a linear equation, assume a value for one of the variables, substitute it into the equation, and solve for the other variable.

### Applications of Linear Equations

- Example: A company manufactures two products A and B, and has 120 hours of labor available. Each unit of A requires 3 hours of labor, and each unit of B requires 2.5 hours.
- Required: Define an equation that states the total work hours used for producing the two units.

### Slope of Linear Equations

- The slope of a linear equation represents the rate of change of the dependent variable with respect to the independent variable.
- Example: Graph the equation 2x + 4y = 16.

### Linear Functions and Their Applications

### Linear Functions

- A linear function has the general form: Y = f(x) = a1x + a0, where a1 and a0 are constants, and a1 â‰ 0.
- A change in the value of y is directly proportional to a change in the value of x, with a constant rate of change represented by the slope a1.
- Example: Imagine that your weekly salary as a salesperson depends on the number of units you sell each week, following the equation y = 3x + 25.

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## Description

This quiz covers the basics of linear equations, including their characteristics and applications. Learn about the definition of linear equations and how to identify them.