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Chapter 9: Problem 51

$$y=-3$$

Short Answer

Expert verified
y = -3

Step by step solution

01

Identify the Given Equation

The given equation is simply: \[ y = -3 \]
02

Interpret the Equation

This equation states that the value of y is equal to -3. Therefore, y is a constant.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Equations
An equation is a mathematical statement that asserts the equality of two expressions. It consists of two expressions separated by an equals sign ( = ). In our exercise, the equation is very straightforward: y = -3This type of equation is called a simple linear equation because it represents a straight line when graphed on a coordinate plane. To solve an equation means to find the value(s) of the variable(s) that make the equation true. In our example, 'y' is the variable, and by interpreting the equation, we've determined that 'y' equals -3.Key points:
  • An equation equates two expressions.
  • The goal is to find the value(s) of the variable(s).
  • In linear equations, we seek a solution that makes the statement true.
Constants
In algebra, a constant is a fixed value. It does not change. In our example, -3 is a constant. When we say that y equals -3, we mean that for this particular equation, y will always have the value of -3. Constants are useful because they provide specific, unchanging values in equations. Here are some important points about constants:
  • They are fixed values, unlike variables which can change.
  • They help in defining relationships in equations.
  • A constant remains the same throughout the entire problem or context in which it is used.
Algebra
Algebra is a branch of mathematics dealing with symbols and the rules for manipulating those symbols. It's about finding the unknown values through equations and expressions. The symbols (like x, y, and z) represent numbers in equations and formulas. Understanding algebra requires knowing how to work with different elements like variables, constants, and operations.In our exercise, we dealt with a simple linear equation: y = -3. Here, we had only one variable, y, and one constant, -3. Key concepts in algebra:
  • Variables: Symbols representing numbers whose value isn't fixed, like 'y' in our example.
  • Constants: Fixed values, like -3, that do not change.
  • Expressions and Equations: Collections of numbers, variables, operations, and an equals sign to show the relationship.
By using these elements effectively, algebra allows us to solve problems and understand the world mathematically.

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Most popular questions from this chapter

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