What Is The Value Of $y = X - 5$ When $x = 9$?A. -4 B. 4 C. 13 D. 9

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Introduction

Linear equations are a fundamental concept in mathematics, and solving them is a crucial skill for students and professionals alike. In this article, we will explore the concept of linear equations, how to solve them, and apply this knowledge to a specific problem.

What are Linear Equations?

A linear equation is an equation in which the highest power of the variable(s) is 1. It can be written in the form of:

ax + b = c

where a, b, and c are constants, and x is the variable.

The Value of y = x - 5

In this problem, we are given the equation y = x - 5, and we need to find the value of y when x = 9.

Step 1: Substitute the Value of x

To find the value of y, we need to substitute the value of x into the equation. In this case, x = 9.

y = 9 - 5

Step 2: Simplify the Equation

Now, we need to simplify the equation by performing the subtraction.

y = 4

Conclusion

Therefore, the value of y = x - 5 when x = 9 is 4.

Why is this Important?

Solving linear equations is an essential skill in mathematics, and it has numerous applications in real-life situations. For example, in physics, linear equations are used to describe the motion of objects, while in economics, they are used to model the behavior of markets.

Real-World Applications

Linear equations have numerous real-world applications, including:

  • Physics: Linear equations are used to describe the motion of objects, such as the trajectory of a projectile or the motion of a pendulum.
  • Economics: Linear equations are used to model the behavior of markets, such as the demand and supply curves.
  • Computer Science: Linear equations are used in computer graphics to create 3D models and animations.
  • Engineering: Linear equations are used to design and optimize systems, such as electrical circuits and mechanical systems.

Tips and Tricks

Here are some tips and tricks to help you solve linear equations:

  • Use the order of operations: When simplifying an equation, use the order of operations (PEMDAS) to ensure that you perform the operations in the correct order.
  • Simplify the equation: Simplify the equation by combining like terms and performing the operations.
  • Check your work: Check your work by plugging the solution back into the original equation to ensure that it is true.

Conclusion

In conclusion, solving linear equations is an essential skill in mathematics, and it has numerous applications in real-life situations. By following the steps outlined in this article, you can solve linear equations with ease and apply this knowledge to a variety of real-world problems.

Frequently Asked Questions

Here are some frequently asked questions about linear equations:

  • What is a linear equation? A linear equation is an equation in which the highest power of the variable(s) is 1.
  • How do I solve a linear equation? To solve a linear equation, substitute the value of the variable into the equation and simplify.
  • What are some real-world applications of linear equations? Linear equations have numerous real-world applications, including physics, economics, computer science, and engineering.

References

  • "Linear Equations" by Khan Academy
  • "Solving Linear Equations" by Math Open Reference
  • "Linear Equations in One Variable" by Purplemath
    Frequently Asked Questions: Linear Equations =====================================================

Q: What is a linear equation?

A: A linear equation is an equation in which the highest power of the variable(s) is 1. It can be written in the form of:

ax + b = c

where a, b, and c are constants, and x is the variable.

Q: How do I solve a linear equation?

A: To solve a linear equation, substitute the value of the variable into the equation and simplify. For example, if we have the equation:

y = x - 5

and we want to find the value of y when x = 9, we would substitute x = 9 into the equation and simplify:

y = 9 - 5 y = 4

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

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

  • Physics: Linear equations are used to describe the motion of objects, such as the trajectory of a projectile or the motion of a pendulum.
  • Economics: Linear equations are used to model the behavior of markets, such as the demand and supply curves.
  • Computer Science: Linear equations are used in computer graphics to create 3D models and animations.
  • Engineering: Linear equations are used to design and optimize systems, such as electrical circuits and mechanical systems.

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. For example:

Linear equation: y = x - 5 Quadratic equation: y = x^2 + 3x - 4

Q: How do I graph a linear equation?

A: To graph a linear equation, you can use the slope-intercept form of the equation, which is:

y = mx + b

where m is the slope and b is the y-intercept. You can then plot the y-intercept and use the slope to find other points on the line.

Q: What is the slope of a linear equation?

A: The slope of a linear equation is a measure of how steep the line is. It can be calculated using the formula:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are two points on the line.

Q: How do I solve a system of linear equations?

A: To solve a system of linear equations, you can use the method of substitution or elimination. For example, if we have the system of equations:

x + y = 3 x - y = 1

we can solve for x and y by adding the two equations together:

2x = 4 x = 2

We can then substitute x = 2 into one of the original equations to solve for y:

2 + y = 3 y = 1

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

A: A linear equation is an equation in which the highest power of the variable(s) is 1, while a nonlinear equation is an equation in which the highest power of the variable(s) is greater than 1. For example:

Linear equation: y = x - 5 Nonlinear equation: y = x^2 + 3x - 4

Q: How do I determine if an equation is linear or nonlinear?

A: To determine if an equation is linear or nonlinear, you can look at the highest power of the variable(s) in the equation. If the highest power is 1, the equation is linear. If the highest power is greater than 1, the equation is nonlinear.

Conclusion

In conclusion, linear equations are a fundamental concept in mathematics, and they have numerous real-world applications. By understanding how to solve linear equations and graph them, you can apply this knowledge to a variety of problems in physics, economics, computer science, and engineering.