The Equation $r = 3c + 5$ Represents The Values Shown In The Table Below.$\[ \begin{tabular}{|c|c|c|c|c|} \hline $c$ & 6 & 8 & 12 & 18 \\ \hline $r$ & 23 & 29 & $? $ & 59 \\ \hline \end{tabular} \\]What Is The Missing Value In The
Introduction
In mathematics, a linear equation is a polynomial equation of degree one, which means it has the form of ax + b = 0, where a and b are constants. In this article, we will explore a linear equation of the form r = 3c + 5, where r and c are variables. We will use this equation to solve for the missing value in a given table.
The Equation and the Table
The equation r = 3c + 5 represents the values shown in the table below.
| c | r |
|---|---|
| 6 | 23 |
| 8 | 29 |
| 12 | ? |
| 18 | 59 |
Understanding the Equation
To understand the equation, let's break it down into its components. The equation is in the form of r = 3c + 5, where r is the dependent variable and c is the independent variable. The coefficient of c is 3, which means that for every unit increase in c, r increases by 3 units. The constant term is 5, which means that r is always 5 units greater than 3c.
Solving for the Missing Value
To solve for the missing value, we need to substitute the value of c into the equation and solve for r. Let's start by substituting c = 12 into the equation.
r = 3(12) + 5 r = 36 + 5 r = 41
Therefore, the missing value in the table is 41.
Conclusion
In this article, we explored a linear equation of the form r = 3c + 5 and used it to solve for the missing value in a given table. We broke down the equation into its components and used it to find the value of r when c = 12. The missing value in the table is 41.
The Importance of Linear Equations
Linear equations are an essential part of mathematics and are used to model real-world relationships. They are used in a wide range of fields, including physics, engineering, economics, and computer science. In this article, we saw how a linear equation can be used to solve for a missing value in a table. This is just one example of how linear equations can be used to model real-world relationships.
Real-World Applications of Linear Equations
Linear equations have many real-world applications. Some examples include:
- Physics: Linear equations are used to model the motion of objects under the influence of gravity. For example, the equation h = 0.5gt^2 + v0t + h0 models the height of an object as a function of time.
- Engineering: Linear equations are used to model the behavior of electrical circuits. For example, the equation V = IR models the voltage across a resistor as a function of current.
- Economics: Linear equations are used to model the behavior of economic systems. For example, the equation C = a + bt models the consumption of a good as a function of income.
- Computer Science: Linear equations are used to model the behavior of algorithms. For example, the equation T = O(n) models the time complexity of an algorithm as a function of input size.
Conclusion
In conclusion, linear equations are an essential part of mathematics and are used to model real-world relationships. They have many real-world applications and are used in a wide range of fields. In this article, we saw how a linear equation can be used to solve for a missing value in a table. This is just one example of how linear equations can be used to model real-world relationships.
References
- Algebra: A Comprehensive Introduction by Michael Artin
- Linear Algebra: A Modern Introduction by David Poole
- Mathematics for Computer Science: A Modern Introduction by Eric Lehman and Tom Leighton
Further Reading
- Linear Equations: A Tutorial by Khan Academy
- Linear Algebra: A Tutorial by MIT OpenCourseWare
- Mathematics for Computer Science: A Tutorial by Stanford University
Glossary
- Linear Equation: A polynomial equation of degree one, which means it has the form of ax + b = 0, where a and b are constants.
- Coefficient: A constant that is multiplied by a variable in an equation.
- Constant Term: A constant that is added to the product of a coefficient and a variable in an equation.
- Independent Variable: A variable that is not dependent on any other variable in an equation.
- Dependent Variable: A variable that is dependent on another variable in an equation.
The Equation of a Linear Relationship: Q&A =============================================
Introduction
In our previous article, we explored a linear equation of the form r = 3c + 5 and used it to solve for the missing value in a given table. In this article, we will answer some frequently asked questions about linear equations and provide additional information to help you understand this important concept in mathematics.
Q: What is a linear equation?
A: A linear equation is a polynomial equation of degree one, which means it has the form of ax + b = 0, where a and b are constants.
Q: What is the difference between a linear equation and a quadratic equation?
A: A linear equation has the form of ax + b = 0, where a and b are constants. A quadratic equation has the form of ax^2 + bx + c = 0, where a, b, and c are constants.
Q: How do I solve a linear equation?
A: To solve a linear equation, you can use the following steps:
- Simplify the equation by combining like terms.
- Isolate the variable by adding or subtracting the same value to both sides of the equation.
- Divide both sides of the equation by the coefficient of the variable.
Q: What is the slope of a linear equation?
A: The slope of a linear equation is the coefficient of the variable. In the equation r = 3c + 5, the slope is 3.
Q: What is the y-intercept of a linear equation?
A: The y-intercept of a linear equation is the constant term. In the equation r = 3c + 5, the y-intercept is 5.
Q: How do I graph a linear equation?
A: To graph a linear equation, you can use the following steps:
- Find the x-intercept by setting the variable equal to zero and solving for the constant term.
- Find the y-intercept by setting the variable equal to zero and solving for the constant term.
- Plot the x-intercept and y-intercept on a coordinate plane.
- Draw a line through the x-intercept and y-intercept.
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 model the motion of objects under the influence of gravity.
- Engineering: Linear equations are used to model the behavior of electrical circuits.
- Economics: Linear equations are used to model the behavior of economic systems.
- Computer Science: Linear equations are used to model the behavior of algorithms.
Q: How do I use linear equations to solve problems?
A: To use linear equations to solve problems, you can follow these steps:
- Identify the variables and constants in the problem.
- Write an equation that represents the problem.
- Solve the equation using the steps outlined above.
- Check your solution by plugging it back into the original equation.
Conclusion
In conclusion, linear equations are an essential part of mathematics and are used to model real-world relationships. They have many real-world applications and are used in a wide range of fields. In this article, we answered some frequently asked questions about linear equations and provided additional information to help you understand this important concept in mathematics.
References
- Algebra: A Comprehensive Introduction by Michael Artin
- Linear Algebra: A Modern Introduction by David Poole
- Mathematics for Computer Science: A Modern Introduction by Eric Lehman and Tom Leighton
Further Reading
- Linear Equations: A Tutorial by Khan Academy
- Linear Algebra: A Tutorial by MIT OpenCourseWare
- Mathematics for Computer Science: A Tutorial by Stanford University
Glossary
- Linear Equation: A polynomial equation of degree one, which means it has the form of ax + b = 0, where a and b are constants.
- Coefficient: A constant that is multiplied by a variable in an equation.
- Constant Term: A constant that is added to the product of a coefficient and a variable in an equation.
- Independent Variable: A variable that is not dependent on any other variable in an equation.
- Dependent Variable: A variable that is dependent on another variable in an equation.