Complete The Table Using The Equation Y = 1 2 X − 1 Y=\frac{1}{2} X-1 Y = 2 1 ​ X − 1 .${ \begin{tabular}{|c|c|} \hline X X X & Y Y Y \ \hline -4 & \ \hline -2 & \ \hline 0 & \ \hline 2 & \ \hline \end{tabular} }$

Introduction to the Equation

The given equation is $y=\frac{1}{2} x-1$. This is a linear equation in the slope-intercept form, where the slope is $\frac{1}{2}$ and the y-intercept is $-1$. The equation represents a straight line on the coordinate plane.

Understanding the Task

We are given a table with values of $x$ and an empty column for $y$. Our task is to complete the table by finding the corresponding values of $y$ for each value of $x$ using the given equation.

Completing the Table

To complete the table, we need to substitute each value of $x$ into the equation $y=\frac{1}{2} x-1$ and solve for $y$.

Substituting $x=-4$

Let's start by substituting $x=-4$ into the equation:

$$y=\frac{1}{2} (-4)-1$$

Simplifying the equation, we get:

$$y=-2-1$$

$$y=-3$$

So, the value of $y$ when $x=-4$ is $-3$.

Substituting $x=-2$

Next, let's substitute $x=-2$ into the equation:

$$y=\frac{1}{2} (-2)-1$$

Simplifying the equation, we get:

$$y=-1-1$$

$$y=-2$$

So, the value of $y$ when $x=-2$ is $-2$.

Substituting $x=0$

Now, let's substitute $x=0$ into the equation:

$$y=\frac{1}{2} (0)-1$$

Simplifying the equation, we get:

$$y=0-1$$

$$y=-1$$

So, the value of $y$ when $x=0$ is $-1$.

Substituting $x=2$

Finally, let's substitute $x=2$ into the equation:

$$y=\frac{1}{2} (2)-1$$

Simplifying the equation, we get:

$$y=1-1$$

$$y=0$$

So, the value of $y$ when $x=2$ is $0$.

Completed Table

Here is the completed table with the values of $y$ for each value of $x$:

$x$	$y$
-4	-3
-2	-2
0	-1
2	0

Conclusion

In this article, we completed the table using the equation $y=\frac{1}{2} x-1$. We substituted each value of $x$ into the equation and solved for $y$ to find the corresponding values. The completed table shows the relationship between the values of $x$ and $y$ as given by the equation.

Key Takeaways

• The equation $y=\frac{1}{2} x-1$ represents a straight line on the coordinate plane.
• To complete the table, we need to substitute each value of $x$ into the equation and solve for $y$.
• The completed table shows the relationship between the values of $x$ and $y$ as given by the equation.

Further Exploration

• Try substituting different values of $x$ into the equation to see how the values of $y$ change.
• Graph the equation on the coordinate plane to visualize the relationship between the values of $x$ and $y$.
• Use the equation to solve for $x$ in terms of $y$ and explore the relationship between the values of $x$ and $y$ in the opposite direction.
  

Introduction

In our previous article, we completed the table using the equation $y=\frac{1}{2} x-1$. We received many questions from readers who wanted to know more about the equation and how to complete the table. In this article, we will answer some of the most frequently asked questions about completing the table.

Q: What is the equation $y=\frac{1}{2} x-1$?

A: The equation $y=\frac{1}{2} x-1$ is a linear equation in the slope-intercept form, where the slope is $\frac{1}{2}$ and the y-intercept is $-1$. This equation represents a straight line on the coordinate plane.

Q: How do I complete the table using the equation?

A: To complete the table, you need to substitute each value of $x$ into the equation and solve for $y$. For example, if you want to find the value of $y$ when $x=-4$, you would substitute $x=-4$ into the equation and solve for $y$.

Q: What if I get a negative value for $y$?

A: If you get a negative value for $y$, it means that the value of $y$ is below the x-axis. This is a common occurrence when working with linear equations.

Q: Can I use the equation to solve for $x$ in terms of $y$?

A: Yes, you can use the equation to solve for $x$ in terms of $y$. To do this, you would need to isolate $x$ on one side of the equation. For example, if you want to solve for $x$ in terms of $y$, you would rearrange the equation to get $x=2y+2$.

Q: How do I graph the equation on the coordinate plane?

A: To graph the equation on the coordinate plane, you would need to plot several points on the graph using the equation. For example, you could plot the points $(0,-1)$, $(2,0)$, and $(-4,-3)$ on the graph. Then, you could draw a line through the points to create the graph.

Q: What if I make a mistake when completing the table?

A: If you make a mistake when completing the table, don't worry! You can always go back and recheck your work. Make sure to double-check your calculations and use a calculator if necessary.

Q: Can I use the equation to solve real-world problems?

A: Yes, you can use the equation to solve real-world problems. For example, if you are a manager at a company and you need to determine the cost of producing a certain number of units, you could use the equation to calculate the cost.

Q: How do I know if the equation is linear or not?

A: To determine if the equation is linear or not, you would need to check if the equation is in the slope-intercept form. If the equation is in the slope-intercept form, it is a linear equation.

Q: Can I use the equation to solve for $y$ in terms of $x$?

A: Yes, you can use the equation to solve for $y$ in terms of $x$. To do this, you would need to isolate $y$ on one side of the equation. For example, if you want to solve for $y$ in terms of $x$, you would rearrange the equation to get $y=\frac{1}{2} x-1$.

Conclusion

In this article, we answered some of the most frequently asked questions about completing the table using the equation $y=\frac{1}{2} x-1$. We hope that this article has been helpful in clarifying any questions you may have had about the equation and how to complete the table.

Key Takeaways

• The equation $y=\frac{1}{2} x-1$ represents a straight line on the coordinate plane.
• To complete the table, you need to substitute each value of $x$ into the equation and solve for $y$.
• You can use the equation to solve for $x$ in terms of $y$ and to solve for $y$ in terms of $x$.
• You can graph the equation on the coordinate plane by plotting several points on the graph using the equation.

Further Exploration

• Try using the equation to solve real-world problems.
• Experiment with different values of $x$ and $y$ to see how the equation changes.
• Use the equation to solve for $x$ and $y$ in terms of each other.