Select The Correct Answer.Find The Value Of $h(-7)$ For The Function Below.$h(x)=5.7-19x$A. -138.7 B. 0.67 C. -127.3 D. 138.7
Introduction
Linear equations are a fundamental concept in mathematics, and solving them is a crucial skill for students to master. In this article, we will focus on solving linear equations in the form of $h(x) = mx + b$, where $m$ is the slope and $b$ is the y-intercept. We will use a specific function, $h(x) = 5.7 - 19x$, to demonstrate how to find the value of $h(-7)$.
Understanding the Function
The given function is $h(x) = 5.7 - 19x$. This is a linear equation in the form of $h(x) = mx + b$, where $m = -19$ and $b = 5.7$. The slope, $m$, represents the rate of change of the function, and the y-intercept, $b$, represents the point where the function intersects the y-axis.
Substituting the Value of x
To find the value of $h(-7)$, we need to substitute $x = -7$ into the function. This means we will replace $x$ with $-7$ in the equation $h(x) = 5.7 - 19x$.
Step-by-Step Solution
- Substitute x = -7 into the function: $h(-7) = 5.7 - 19(-7)$
- Simplify the equation: $h(-7) = 5.7 + 133$
- Combine like terms: $h(-7) = 138.7$
Conclusion
In this article, we have demonstrated how to find the value of $h(-7)$ for the function $h(x) = 5.7 - 19x$. By substituting $x = -7$ into the function and simplifying the equation, we arrived at the solution $h(-7) = 138.7$. This is a simple yet important concept in mathematics, and we hope this article has provided a clear and concise explanation of how to solve linear equations.
Answer
The correct answer is:
- D. 138.7
Discussion
This problem is a great example of how to apply the concept of linear equations to real-world scenarios. In mathematics, we often encounter problems that require us to find the value of a function at a specific point. By following the steps outlined in this article, we can confidently solve these types of problems and arrive at the correct solution.
Additional Resources
For more information on linear equations and how to solve them, we recommend checking out the following resources:
- Khan Academy: Linear Equations
- Mathway: Linear Equations
- Wolfram Alpha: Linear Equations
Introduction
In our previous article, we discussed how to solve linear equations in the form of $h(x) = mx + b$. We used a specific function, $h(x) = 5.7 - 19x$, to demonstrate how to find the value of $h(-7)$. In this article, we will provide a Q&A guide to help you better understand and apply the concept of 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. In other words, it is an equation that can be written in the form of $h(x) = mx + b$, where $m$ is the slope and $b$ is the y-intercept.
Q: What is the slope (m) in a linear equation?
A: The slope (m) in a linear equation represents the rate of change of the function. It tells us how much the function changes for a one-unit change in the input variable.
Q: What is the y-intercept (b) in a linear equation?
A: The y-intercept (b) in a linear equation represents the point where the function intersects the y-axis. It is the value of the function when the input variable is 0.
Q: How do I find the value of a linear equation at a specific point?
A: To find the value of a linear equation at a specific point, you need to substitute the value of the input variable into the equation and simplify. For example, if you want to find the value of $h(-7)$ for the function $h(x) = 5.7 - 19x$, you would substitute $x = -7$ into the equation and simplify.
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. In other words, a linear equation can be written in the form of $h(x) = mx + b$, while a quadratic equation can be written in the form of $h(x) = ax^2 + bx + c$.
Q: How do I determine if an equation is linear or quadratic?
A: To determine if an equation is linear or quadratic, you need to look at the highest power of the variable(s). If the highest power is 1, the equation is linear. If the highest power is 2, the equation is quadratic.
Q: What are some common applications of linear equations?
A: Linear equations have many real-world applications, including:
- Modeling population growth
- Calculating the cost of goods
- Determining the distance between two points
- Finding the area of a rectangle
Conclusion
In this article, we have provided a Q&A guide to help you better understand and apply the concept of linear equations. We hope this guide has been helpful in answering your questions and providing you with a deeper understanding of linear equations.
Additional Resources
For more information on linear equations and how to solve them, we recommend checking out the following resources:
- Khan Academy: Linear Equations
- Mathway: Linear Equations
- Wolfram Alpha: Linear Equations
These resources provide a wealth of information and examples to help you master the concept of linear equations.
Frequently Asked Questions
- 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 determine if an equation is linear or quadratic?
- A: To determine if an equation is linear or quadratic, you need to look at the highest power of the variable(s). If the highest power is 1, the equation is linear. If the highest power is 2, the equation is quadratic.
- Q: What are some common applications of linear equations?
- A: Linear equations have many real-world applications, including modeling population growth, calculating the cost of goods, determining the distance between two points, and finding the area of a rectangle.