Fill In The Missing Values In The Table For The Equation $y=\frac{3}{2}x-2$.$\[ \begin{array}{|c|c|} \hline x & Y \\ \hline -2 & A \\ \hline -1 & B \\ \hline 0 & C \\ \hline 1 & D \\ \hline 2 & E

Introduction

In this article, we will explore the concept of solving for missing values in a linear equation. We will use the equation $y=\frac{3}{2}x-2$ as an example and fill in the missing values in the table. This will help us understand how to work with linear equations and how to use them to solve problems.

Understanding Linear Equations

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 $y=mx+b$, where $m$ is the slope and $b$ is the y-intercept. The equation $y=\frac{3}{2}x-2$ is a linear equation because it can be written in this form.

The Equation $y=\frac{3}{2}x-2$

The equation $y=\frac{3}{2}x-2$ is a linear equation with a slope of $\frac{3}{2}$ and a y-intercept of -2. This means that for every 1 unit increase in $x$, $y$ will increase by $\frac{3}{2}$ units.

Filling in the Missing Values

Now that we understand the equation $y=\frac{3}{2}x-2$, we can fill in the missing values in the table.

Table

x	y
-2	a
-1	b
0	c
1	d
2	e

To fill in the missing values, we can plug in the values of $x$ into the equation $y=\frac{3}{2}x-2$ and solve for $y$.

Solving for $y$

• For $x=-2$, we have: $y=\frac{3}{2}(-2)-2=-6$
• For $x=-1$, we have: $y=\frac{3}{2}(-1)-2=-3$
• For $x=0$, we have: $y=\frac{3}{2}(0)-2=-2$
• For $x=1$, we have: $y=\frac{3}{2}(1)-2=-\frac{1}{2}$
• For $x=2$, we have: $y=\frac{3}{2}(2)-2=1$

Filled-in Table

x	y
-2	-6
-1	-3
0	-2
1	-0.5
2	1

Conclusion

In this article, we filled in the missing values in the table for the equation $y=\frac{3}{2}x-2$. We used the equation to solve for $y$ for each value of $x$ and filled in the table with the corresponding values. This demonstrates how to work with linear equations and how to use them to solve problems.

Tips and Tricks

• When working with linear equations, make sure to identify the slope and y-intercept.
• Use the equation to solve for $y$ for each value of $x$.
• Fill in the table with the corresponding values.

Common Mistakes

• Failing to identify the slope and y-intercept.
• Not using the equation to solve for $y$ for each value of $x$.
• Not filling in the table with the corresponding values.

Real-World Applications

Linear equations have many real-world applications, including:

• Modeling population growth
• Calculating interest rates
• Determining the cost of goods
• Solving problems in physics and engineering

Practice Problems

1. Fill in the missing values in the table for the equation $y=2x+1$.
2. Solve for $y$ for each value of $x$ in the equation $y=-3x+2$.
3. Fill in the table with the corresponding values for the equation $y=\frac{1}{2}x-1$.

Answer Key

1.	x	y
-2	-3
-1	0
0	1
1	3
2	5
2.	x	y
---	---
-2	7
-1	4
0	2
1	0
2	-2
3.	x	y
---	---
-2	-2
-1	-1.5
0	-1
1	0
2	1

Conclusion

$$$$$$

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 $y=mx+b$, 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 change in $y$ for a one-unit change in $x$. It is represented by the letter $m$ in the equation $y=mx+b$.

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

A: The y-intercept of a linear equation is the value of $y$ when $x$ is equal to 0. It is represented by the letter $b$ in the equation $y=mx+b$.

Q: How do I solve a linear equation?

A: To solve a linear equation, you can use the following steps:

1. Identify the slope and y-intercept of the equation.
2. Plug in the values of $x$ into the equation and solve for $y$.
3. Fill in the table with the corresponding values.

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 linear equations to solve real-world problems?

A: Yes, linear equations can be used to solve a wide range of real-world problems, including modeling population growth, calculating interest rates, determining the cost of goods, and solving problems in physics and engineering.

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

A: Some common mistakes to avoid when working with linear equations include:

• Failing to identify the slope and y-intercept.
• Not using the equation to solve for $y$ for each value of $x$.
• Not filling in the table with the corresponding values.

Q: How can I practice working with linear equations?

A: You can practice working with linear equations by:

• Filling in the missing values in the table for a given equation.
• Solving for $y$ for each value of $x$ in a given equation.
• Using linear equations to solve real-world problems.

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

A: Some real-world applications of linear equations include:

• Modeling population growth.
• Calculating interest rates.
• Determining the cost of goods.
• Solving problems in physics and engineering.

Q: Can I use linear equations to solve problems in other fields?

A: Yes, linear equations can be used to solve problems in a wide range of fields, including business, economics, and social sciences.

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