Select The Correct Answer.Find The Value Of H ( − 7 H(-7 H ( − 7 ] For The Function Below. H ( X ) = 5.7 − 19 X H(x) = 5.7 - 19x H ( X ) = 5.7 − 19 X A. -138.7 B. -127.3 C. 138.7 D. 0.67

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 illustrate the steps involved in solving linear equations.

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.

Finding the Value of $h(-7)$

To find the value of $h(-7)$, we need to substitute $x = -7$ into the function $h(x) = 5.7 - 19x$. This will give us the value of the function at $x = -7$.

Step 1: Substitute $x = -7$ into the function

$h(-7) = 5.7 - 19(-7)$

Step 2: Simplify the expression

To simplify the expression, we need to multiply $-19$ by $-7$. This will give us a positive value.

$h(-7) = 5.7 + 133$

Step 3: Add the values

Now, we need to add $5.7$ and $133$ to get the final value of $h(-7)$.

$h(-7) = 138.7$

Conclusion

In this article, we have solved a linear equation in the form of $h(x) = mx + b$. We have used the function $h(x) = 5.7 - 19x$ to illustrate the steps involved in solving linear equations. We have found the value of $h(-7)$ by substituting $x = -7$ into the function and simplifying the expression. The final value of $h(-7)$ is $138.7$.

Answer

The correct answer is:

• C. 138.7

Discussion

This problem is a great example of how to solve linear equations in the form of $h(x) = mx + b$. The function $h(x) = 5.7 - 19x$ is a simple linear equation, and solving it requires only basic algebraic manipulations. The key concept here is to substitute the given value of $x$ into the function and simplify the expression to get the final value.

Tips and Tricks

• When solving linear equations, make sure to substitute the given value of $x$ into the function.
• Simplify the expression by combining like terms.
• Add or subtract the values to get the final answer.

Related Topics

• Solving quadratic equations
• Graphing linear equations
• Systems of linear equations

Conclusion

$$$$

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 illustrate the steps involved in solving linear equations. In this article, we will provide a Q&A guide to help students better understand the concept of solving linear equations.

Q: What is a linear equation?

A: A linear equation is an equation in which the highest power of the variable (usually $x$) is 1. It 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 of a linear equation?

A: The slope of a linear equation is the rate of change of the function. It is represented by the coefficient of the variable (usually $x$). In the function $h(x) = 5.7 - 19x$, the slope is $-19$.

Q: What is the y-intercept of a linear equation?

A: The y-intercept of a linear equation is the point where the function intersects the y-axis. It is represented by the constant term in the function. In the function $h(x) = 5.7 - 19x$, the y-intercept is $5.7$.

Q: How do I solve a linear equation?

A: To solve a linear equation, you need to substitute the given value of $x$ into the function and simplify the expression to get the final value.

Q: What if the equation has a negative slope?

A: If the equation has a negative slope, it means that the function is decreasing as $x$ increases. To solve the equation, you need to substitute the given value of $x$ into the function and simplify the expression to get the final value.

Q: Can I use a calculator to solve linear equations?

A: Yes, you can use a calculator to solve linear equations. However, it's always a good idea to check your work by hand to make sure you get the correct answer.

Q: What if I get a negative value for the slope?

A: If you get a negative value for the slope, it means that the function is increasing as $x$ decreases. To solve the equation, you need to substitute the given value of $x$ into the function and simplify the expression to get the final value.

Q: Can I graph a linear equation?

A: Yes, you can graph a linear equation. To graph a linear equation, you need to plot the points on a coordinate plane and draw a line through them.

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 (usually $x$) is 1. A quadratic equation is an equation in which the highest power of the variable (usually $x$) is 2.

Conclusion

In conclusion, solving linear equations is a crucial skill for students to master. By following the steps outlined in this article, students can solve linear equations in the form of $h(x) = mx + b$. The key concept here is to substitute the given value of $x$ into the function and simplify the expression to get the final value.

Tips and Tricks

• Make sure to substitute the given value of $x$ into the function.
• Simplify the expression by combining like terms.
• Add or subtract the values to get the final answer.

Related Topics

• Solving quadratic equations
• Graphing linear equations
• Systems of linear equations

Common Mistakes

• Not substituting the given value of $x$ into the function.
• Not simplifying the expression by combining like terms.
• Not adding or subtracting the values to get the final answer.

Conclusion

In conclusion, solving linear equations is a crucial skill for students to master. By following the steps outlined in this article, students can solve linear equations in the form of $h(x) = mx + b$. The key concept here is to substitute the given value of $x$ into the function and simplify the expression to get the final value.