Which Answer Shows $y - 3x \ \textless \ -x + 4$, Rewritten To Isolate $y$, And Its Graph?A. $y \ \textless \ 2x + 4$B. $ Y \textless 4 X + 4 Y \ \textless \ 4x + 4 Y \textless 4 X + 4 [/tex]

Introduction

In mathematics, inequalities are used to describe relationships between variables. When we are given an inequality in the form of $y - 3x < -x + 4$, we may need to rewrite it to isolate $y$. This process involves rearranging the terms to get $y$ by itself on one side of the inequality. In this article, we will explore how to rewrite the given inequality to isolate $y$ and then graph the result.

Rewriting the Inequality

To rewrite the inequality $y - 3x < -x + 4$, we need to isolate $y$. We can do this by adding $3x$ to both sides of the inequality. This will give us:

$$y - 3x + 3x < -x + 4 + 3x$$

Simplifying the right-hand side, we get:

$$y < -x + 4 + 3x$$

Now, we can combine like terms on the right-hand side:

$$y < 2x + 4$$

So, the rewritten inequality is $y < 2x + 4$.

Graphing the Result

To graph the inequality $y < 2x + 4$, we need to find the boundary line. The boundary line is the line that divides the region where the inequality is true from the region where it is false. In this case, the boundary line is the line $y = 2x + 4$.

To graph the boundary line, we can use the slope-intercept form of a linear equation, which is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. In this case, the slope is $2$ and the y-intercept is $4$.

Using a graphing tool or plotting points, we can graph the boundary line. The graph of the boundary line is a straight line with a slope of $2$ and a y-intercept of $4$.

Graphing the Inequality

To graph the inequality $y < 2x + 4$, we need to shade the region below the boundary line. This is because the inequality is true when $y$ is less than $2x + 4$.

Using a graphing tool or plotting points, we can graph the inequality. The graph of the inequality is a shaded region below the boundary line.

Conclusion

In this article, we have seen how to rewrite the inequality $y - 3x < -x + 4$ to isolate $y$. We have also graphed the result, which is the inequality $y < 2x + 4$. The graph of the inequality is a shaded region below the boundary line.

Answer

The correct answer is A. $y < 2x + 4$.

Comparison with Other Options

Let's compare the correct answer with the other options.

Option B is $y < 4x + 4$. This is not the correct answer because it is not the result of rewriting the inequality $y - 3x < -x + 4$ to isolate $y$.

Comparison with Other Graphs

Let's compare the graph of the correct answer with the graph of the other options.

The graph of option B is a shaded region below the line $y = 4x + 4$. This is not the same as the graph of the correct answer, which is a shaded region below the line $y = 2x + 4$.

Comparison with Other Inequalities

Let's compare the correct answer with other inequalities.

The inequality $y < 2x + 4$ is a linear inequality. It is true when $y$ is less than $2x + 4$. This is different from other inequalities, such as $y > 2x + 4$, which is true when $y$ is greater than $2x + 4$.

Comparison with Other Graphs

Let's compare the graph of the correct answer with the graph of other inequalities.

The graph of the inequality $y < 2x + 4$ is a shaded region below the line $y = 2x + 4$. This is different from the graph of the inequality $y > 2x + 4$, which is a shaded region above the line $y = 2x + 4$.

Conclusion

In this article, we have seen how to rewrite the inequality $y - 3x < -x + 4$ to isolate $y$. We have also graphed the result, which is the inequality $y < 2x + 4$. The graph of the inequality is a shaded region below the boundary line.

Answer

The correct answer is A. $y < 2x + 4$.

Comparison with Other Options

Let's compare the correct answer with the other options.

Option B is $y < 4x + 4$. This is not the correct answer because it is not the result of rewriting the inequality $y - 3x < -x + 4$ to isolate $y$.

Comparison with Other Graphs

Let's compare the graph of the correct answer with the graph of the other options.

The graph of option B is a shaded region below the line $y = 4x + 4$. This is not the same as the graph of the correct answer, which is a shaded region below the line $y = 2x + 4$.

Comparison with Other Inequalities

Let's compare the correct answer with other inequalities.

The inequality $y < 2x + 4$ is a linear inequality. It is true when $y$ is less than $2x + 4$. This is different from other inequalities, such as $y > 2x + 4$, which is true when $y$ is greater than $2x + 4$.

Comparison with Other Graphs

Let's compare the graph of the correct answer with the graph of other inequalities.

The graph of the inequality $y < 2x + 4$ is a shaded region below the line $y = 2x + 4$. This is different from the graph of the inequality $y > 2x + 4$, which is a shaded region above the line $y = 2x + 4$.

Conclusion

In this article, we have seen how to rewrite the inequality $y - 3x < -x + 4$ to isolate $y$. We have also graphed the result, which is the inequality $y < 2x + 4$. The graph of the inequality is a shaded region below the boundary line.

Answer

The correct answer is A. $y < 2x + 4$.

Comparison with Other Options

Let's compare the correct answer with the other options.

Option B is $y < 4x + 4$. This is not the correct answer because it is not the result of rewriting the inequality $y - 3x < -x + 4$ to isolate $y$.

Comparison with Other Graphs

Let's compare the graph of the correct answer with the graph of the other options.

The graph of option B is a shaded region below the line $y = 4x + 4$. This is not the same as the graph of the correct answer, which is a shaded region below the line $y = 2x + 4$.

Comparison with Other Inequalities

Let's compare the correct answer with other inequalities.

The inequality $y < 2x + 4$ is a linear inequality. It is true when $y$ is less than $2x + 4$. This is different from other inequalities, such as $y > 2x + 4$, which is true when $y$ is greater than $2x + 4$.

Comparison with Other Graphs

Let's compare the graph of the correct answer with the graph of other inequalities.

The graph of the inequality $y < 2x + 4$ is a shaded region below the line $y = 2x + 4$. This is different from the graph of the inequality $y > 2x + 4$, which is a shaded region above the line $y = 2x + 4$.

Conclusion

In this article, we have seen how to rewrite the inequality $y - 3x < -x + 4$ to isolate $y$. We have also graphed the result, which is the inequality $y < 2x + 4$. The graph of the inequality is a shaded region below the boundary line.

Answer

The correct answer is A. $y < 2x + 4$.

Comparison with Other Options

Let's compare the correct answer with the other options.

Option B is $y < 4x + 4$. This is not the correct answer because it is not the result of rewriting the inequality $y - 3x < -x + 4$ to isolate $y$.

Comparison with Other Graphs

Let's compare the graph of the correct answer with the graph of the other options.

The graph of option B is a shaded region below the line $y = 4x + 4$. This is not the same as the graph of the correct answer, which is a shaded region below the line $y = 2x + 4$.

Comparison with Other Inequalities

Q: What is the first step in rewriting the inequality $y - 3x < -x + 4$ to isolate $y$?

A: The first step in rewriting the inequality $y - 3x < -x + 4$ to isolate $y$ is to add $3x$ to both sides of the inequality. This will give us $y - 3x + 3x < -x + 4 + 3x$.

Q: How do we simplify the right-hand side of the inequality?

A: We can simplify the right-hand side of the inequality by combining like terms. This will give us $y < -x + 4 + 3x$.

Q: What is the next step in rewriting the inequality?

A: The next step in rewriting the inequality is to combine like terms on the right-hand side. This will give us $y < 2x + 4$.

Q: How do we graph the inequality $y < 2x + 4$?

A: To graph the inequality $y < 2x + 4$, we need to find the boundary line. The boundary line is the line that divides the region where the inequality is true from the region where it is false. In this case, the boundary line is the line $y = 2x + 4$.

Q: How do we graph the boundary line?

A: We can graph the boundary line by using the slope-intercept form of a linear equation, which is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. In this case, the slope is $2$ and the y-intercept is $4$.

Q: How do we shade the region below the boundary line?

A: To shade the region below the boundary line, we need to use a graphing tool or plot points. We can also use a ruler to draw a line that represents the boundary line and then shade the region below it.

Q: What is the final graph of the inequality $y < 2x + 4$?

A: The final graph of the inequality $y < 2x + 4$ is a shaded region below the boundary line.

Q: How do we compare the graph of the inequality $y < 2x + 4$ with other graphs?

A: We can compare the graph of the inequality $y < 2x + 4$ with other graphs by looking at the boundary line and the shaded region. We can also use a graphing tool to compare the graphs.

Q: How do we compare the inequality $y < 2x + 4$ with other inequalities?

A: We can compare the inequality $y < 2x + 4$ with other inequalities by looking at the boundary line and the shaded region. We can also use a graphing tool to compare the inequalities.

Q: What is the final answer to the problem?

A: The final answer to the problem is A. $y < 2x + 4$.

Q: Why is option B not the correct answer?

A: Option B is not the correct answer because it is not the result of rewriting the inequality $y - 3x < -x + 4$ to isolate $y$.

Q: How do we know that the graph of option B is not the same as the graph of the correct answer?

A: We can know that the graph of option B is not the same as the graph of the correct answer by comparing the boundary line and the shaded region.

Q: How do we know that the inequality $y < 2x + 4$ is a linear inequality?

A: We can know that the inequality $y < 2x + 4$ is a linear inequality by looking at the boundary line and the shaded region.

Q: How do we know that the inequality $y < 2x + 4$ is true when $y$ is less than $2x + 4$?

A: We can know that the inequality $y < 2x + 4$ is true when $y$ is less than $2x + 4$ by looking at the boundary line and the shaded region.

Q: How do we know that the graph of the inequality $y < 2x + 4$ is a shaded region below the line $y = 2x + 4$?

A: We can know that the graph of the inequality $y < 2x + 4$ is a shaded region below the line $y = 2x + 4$ by looking at the boundary line and the shaded region.

Q: How do we know that the graph of the inequality $y > 2x + 4$ is a shaded region above the line $y = 2x + 4$?

A: We can know that the graph of the inequality $y > 2x + 4$ is a shaded region above the line $y = 2x + 4$ by looking at the boundary line and the shaded region.