Which Ordered Pair Is A Solution To Y = 4.5 X + 20 Y = 4.5x + 20 Y = 4.5 X + 20 ?A. ( 5 , 40 (5, 40 ( 5 , 40 ] B. ( 7 , 52 (7, 52 ( 7 , 52 ] C. ( 10 , 25 (10, 25 ( 10 , 25 ] D. ( 12 , 74 (12, 74 ( 12 , 74 ]

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Introduction to Linear Equations

Linear equations are a fundamental concept in mathematics, and they play a crucial role in various fields such as physics, engineering, and economics. A linear equation is an equation in which the highest power of the variable(s) is 1. In this article, we will focus on solving linear equations of the form y = mx + b, where m is the slope and b is the y-intercept.

Understanding the Problem

The problem asks us to find the ordered pair that is a solution to the linear equation y = 4.5x + 20. To solve this problem, we need to substitute the given values of x and y from each option into the equation and check if the equation holds true.

Option A: (5, 40)

Let's substitute x = 5 and y = 40 into the equation y = 4.5x + 20.

y = 4.5(5) + 20 y = 22.5 + 20 y = 42.5

Since 42.5 is not equal to 40, option A is not a solution to the equation.

Option B: (7, 52)

Let's substitute x = 7 and y = 52 into the equation y = 4.5x + 20.

y = 4.5(7) + 20 y = 31.5 + 20 y = 51.5

Since 51.5 is not equal to 52, option B is not a solution to the equation.

Option C: (10, 25)

Let's substitute x = 10 and y = 25 into the equation y = 4.5x + 20.

y = 4.5(10) + 20 y = 45 + 20 y = 65

Since 65 is not equal to 25, option C is not a solution to the equation.

Option D: (12, 74)

Let's substitute x = 12 and y = 74 into the equation y = 4.5x + 20.

y = 4.5(12) + 20 y = 54 + 20 y = 74

Since 74 is equal to 74, option D is a solution to the equation.

Conclusion

In this article, we have discussed how to solve linear equations of the form y = mx + b. We have also applied this concept to find the ordered pair that is a solution to the equation y = 4.5x + 20. By substituting the given values of x and y from each option into the equation, we have found that option D, (12, 74), is the correct solution.

Tips and Tricks

  • When solving linear equations, make sure to substitute the given values of x and y into the equation correctly.
  • Use a calculator to check if the equation holds true.
  • If the equation does not hold true, try substituting different values of x and y to find the correct solution.

Real-World Applications

Linear equations have numerous real-world applications, such as:

  • 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 bridges, buildings, and electronic circuits.
  • Economics: Linear equations are used to model economic systems and make predictions about future trends.

Common Mistakes

  • Not substituting the given values of x and y into the equation correctly.
  • Not using a calculator to check if the equation holds true.
  • Not trying different values of x and y to find the correct solution.

Conclusion

In conclusion, solving linear equations is an essential skill in mathematics, and it has numerous real-world applications. By following the steps outlined in this article, you can find the ordered pair that is a solution to a linear equation. Remember to substitute the given values of x and y into the equation correctly, use a calculator to check if the equation holds true, and try different values of x and y to find the correct solution.

Introduction

In our previous article, we discussed how to solve linear equations of the form y = mx + b. We also applied this concept to find the ordered pair that is a solution to the equation y = 4.5x + 20. In this article, we will answer some frequently asked questions about solving 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 is typically written in the form y = mx + b, where m is the slope and b is the y-intercept.

Q: How do I solve a linear equation?

A: To solve a linear equation, you need to isolate the variable (in this case, y) 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 slope (m) in a linear equation?

A: The slope (m) in a linear equation is a measure of how steep the line is. It is calculated by dividing the change in y (rise) by the change in x (run).

Q: What is the y-intercept (b) in a linear equation?

A: The y-intercept (b) in a linear equation is the point where the line crosses the y-axis. It is the value of y when x is equal to 0.

Q: How do I find the ordered pair that is a solution to a linear equation?

A: To find the ordered pair that is a solution to a linear equation, you need to substitute the given values of x and y into the equation and check if the equation holds true.

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: Can I use a calculator to solve linear equations?

A: Yes, you can use a calculator to solve linear equations. In fact, calculators can be very helpful in solving linear equations, especially when the numbers are large or complex.

Q: What are some common mistakes to avoid when solving linear equations?

A: Some common mistakes to avoid when solving linear equations include:

  • Not substituting the given values of x and y into the equation correctly
  • Not using a calculator to check if the equation holds true
  • Not trying different values of x and y to find the correct solution

Q: How do I graph a linear equation?

A: To graph a linear equation, you need to plot two points on the graph and draw a line through them. You can also use a graphing calculator to graph the equation.

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

A: Linear equations have numerous real-world applications, such as:

  • 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 bridges, buildings, and electronic circuits.
  • Economics: Linear equations are used to model economic systems and make predictions about future trends.

Conclusion

In conclusion, solving linear equations is an essential skill in mathematics, and it has numerous real-world applications. By following the steps outlined in this article, you can answer some frequently asked questions about solving linear equations. Remember to substitute the given values of x and y into the equation correctly, use a calculator to check if the equation holds true, and try different values of x and y to find the correct solution.