Solve For \[$ Y \$\] In The Equation:$\[ \begin{array}{r} -x + Y = 6 \\ \end{array} \\]Express \[$ Y \$\] In Terms Of \[$ X \$\].

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Introduction

In mathematics, solving linear equations is a fundamental concept that helps us find the value of a variable in terms of another variable. In this article, we will focus on solving a simple linear equation and expressing y in terms of x. We will use the given equation: -x + y = 6, and solve for y in terms of x.

Understanding the Equation

The given equation is a linear equation in two variables, x and y. The equation is in the form of -x + y = 6, where -x is the coefficient of x, and y is the variable we want to solve for. The constant term on the right-hand side of the equation is 6.

Solving for y

To solve for y, we need to isolate y on one side of the equation. We can do this by adding x to both sides of the equation, which will eliminate the -x term. This will give us:

y = 6 + x

Expressing y in Terms of x

Now that we have solved for y, we can express y in terms of x. This means that we can write y as a function of x. In this case, y is equal to 6 plus x. We can write this as:

y = f(x) = 6 + x

Graphical Representation

To visualize the relationship between x and y, we can graph the equation y = 6 + x. The graph will be a straight line with a slope of 1 and a y-intercept of 6.

Interpretation

The equation y = 6 + x tells us that for every value of x, there is a corresponding value of y. The value of y is equal to 6 plus the value of x. This means that if we know the value of x, we can find the value of y by plugging x into the equation.

Example

Let's say we want to find the value of y when x = 2. We can plug x = 2 into the equation y = 6 + x to get:

y = 6 + 2
y = 8

Therefore, when x = 2, y = 8.

Conclusion

In this article, we solved a simple linear equation and expressed y in terms of x. We used the equation -x + y = 6 and solved for y by adding x to both sides of the equation. We then expressed y in terms of x as y = 6 + x. We also graphed the equation and interpreted the results. Finally, we provided an example of how to use the equation to find the value of y when x is given.

Key Takeaways

  • Solving linear equations is a fundamental concept in mathematics.
  • To solve for y, we need to isolate y on one side of the equation.
  • We can express y in terms of x by writing y as a function of x.
  • The equation y = 6 + x tells us that for every value of x, there is a corresponding value of y.
  • We can use the equation to find the value of y when x is given.

Further Reading

If you want to learn more about solving linear equations and expressing y in terms of x, I recommend checking out the following resources:

  • Khan Academy: Solving Linear Equations
  • Mathway: Solving Linear Equations
  • Wolfram Alpha: Solving Linear Equations

References

  • [1] "Algebra and Trigonometry" by Michael Sullivan
  • [2] "College Algebra" by James Stewart
  • [3] "Linear Algebra and Its Applications" by Gilbert Strang
    Solving Linear Equations: Q&A =============================

Introduction

In our previous article, we solved a simple linear equation and expressed y in terms of x. We also provided an example of how to use the equation to find the value of y when x is given. In this article, we will answer some frequently asked questions about solving linear equations and expressing y in terms of x.

Q: What is a linear equation?

A: A linear equation is an equation in which the highest power of the variable(s) is 1. In other words, it is an equation in which the variable(s) are not raised to a power greater than 1.

Q: How do I solve a linear equation?

A: To solve a linear equation, you need to isolate the variable on one side of the equation. You can do this by adding, subtracting, multiplying, or dividing both sides of the equation by the same value.

Q: What is the difference between a linear equation and a quadratic equation?

A: A linear equation is an equation in which the highest power of the variable(s) is 1, while a quadratic equation is an equation in which the highest power of the variable(s) is 2.

Q: How do I express y in terms of x?

A: To express y in terms of x, you need to solve the equation for y. This means that you need to isolate y on one side of the equation.

Q: What is the equation y = 6 + x?

A: The equation y = 6 + x is a linear equation in which y is expressed in terms of x. It tells us that for every value of x, there is a corresponding value of y.

Q: How do I graph the equation y = 6 + x?

A: To graph the equation y = 6 + x, you need to plot the points (x, y) that satisfy the equation. Since the equation is a linear equation, the graph will be a straight line with a slope of 1 and a y-intercept of 6.

Q: What is the slope of the graph of the equation y = 6 + x?

A: The slope of the graph of the equation y = 6 + x is 1. This means that for every 1 unit increase in x, there is a corresponding 1 unit increase in y.

Q: What is the y-intercept of the graph of the equation y = 6 + x?

A: The y-intercept of the graph of the equation y = 6 + x is 6. This means that when x = 0, y = 6.

Q: Can I use the equation y = 6 + x to find the value of y when x is given?

A: Yes, you can use the equation y = 6 + x to find the value of y when x is given. Simply plug the value of x into the equation and solve for y.

Q: What are some real-world applications of linear equations?

A: Linear equations have many real-world applications, including:

  • Physics: Linear equations are used to describe the motion of objects under constant acceleration.
  • Engineering: Linear equations are used to design and optimize systems, such as electrical circuits and mechanical systems.
  • Economics: Linear equations are used to model economic systems and make predictions about future economic trends.

Conclusion

In this article, we answered some frequently asked questions about solving linear equations and expressing y in terms of x. We also provided examples and explanations to help illustrate the concepts. We hope that this article has been helpful in clarifying any confusion you may have had about linear equations.

Key Takeaways

  • A linear equation is an equation in which the highest power of the variable(s) is 1.
  • To solve a linear equation, you need to isolate the variable on one side of the equation.
  • To express y in terms of x, you need to solve the equation for y.
  • The equation y = 6 + x is a linear equation in which y is expressed in terms of x.
  • The graph of the equation y = 6 + x is a straight line with a slope of 1 and a y-intercept of 6.

Further Reading

If you want to learn more about solving linear equations and expressing y in terms of x, I recommend checking out the following resources:

  • Khan Academy: Solving Linear Equations
  • Mathway: Solving Linear Equations
  • Wolfram Alpha: Solving Linear Equations

References

  • [1] "Algebra and Trigonometry" by Michael Sullivan
  • [2] "College Algebra" by James Stewart
  • [3] "Linear Algebra and Its Applications" by Gilbert Strang