On A Piece Of Paper, Graph $y - 5 \ \textgreater \ 2x - 10$. Then Determine Which Answer Choice Matches The Graph You Drew.A. Graph A B. Graph B C. Graph C D. Graph D

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Understanding the Inequality

To graph the inequality $y - 5 \ \textgreater \ 2x - 10$, we need to first rewrite it in a more familiar form. By adding 5 to both sides, we get $y \ \textgreater \ 2x - 5$. This is a linear inequality in slope-intercept form, where the slope is 2 and the y-intercept is -5.

Graphing the Inequality

To graph the inequality, we need to first graph the corresponding equation $y = 2x - 5$. This is a line with a slope of 2 and a y-intercept of -5. We can graph this line by plotting two points on the line and drawing a line through them.

Finding the Solution Region

Since the inequality is $y \ \textgreater \ 2x - 5$, we need to find the region above the line $y = 2x - 5$. This means that any point above the line is a solution to the inequality.

Graphing the Solution Region

To graph the solution region, we can draw a dashed line to represent the boundary of the solution region. We can also shade the region above the line to indicate that it is the solution region.

Comparing with Answer Choices

Now that we have graphed the inequality, we can compare it with the answer choices to determine which one matches the graph.

Graph A

Graph A is a line with a slope of 2 and a y-intercept of -5. However, it is a solid line, which means it represents an equation, not an inequality. Therefore, Graph A does not match the graph of the inequality.

Graph B

Graph B is a line with a slope of 2 and a y-intercept of -5. However, it is a dashed line, which means it represents an inequality. However, the inequality is $y \ \textless \ 2x - 5$, not $y \ \textgreater \ 2x - 5$. Therefore, Graph B does not match the graph of the inequality.

Graph C

Graph C is a line with a slope of 2 and a y-intercept of -5. However, it is a solid line, which means it represents an equation, not an inequality. However, the inequality is $y \ \textgreater \ 2x - 5$, which is the same as the original inequality. Therefore, Graph C does not match the graph of the inequality.

Graph D

Graph D is a line with a slope of 2 and a y-intercept of -5. However, it is a dashed line, which means it represents an inequality. The inequality is $y \ \textgreater \ 2x - 5$, which is the same as the original inequality. Therefore, Graph D matches the graph of the inequality.

Conclusion

Based on the graph of the inequality $y - 5 \ \textgreater \ 2x - 10$, we can conclude that the answer choice that matches the graph is Graph D.

Step-by-Step Solution

Here is a step-by-step solution to the problem:

1. Rewrite the inequality in a more familiar form by adding 5 to both sides: $y \ \textgreater \ 2x - 5$.
2. Graph the corresponding equation $y = 2x - 5$ by plotting two points on the line and drawing a line through them.
3. Find the solution region by determining the region above the line $y = 2x - 5$.
4. Graph the solution region by drawing a dashed line to represent the boundary of the solution region and shading the region above the line.
5. Compare the graph with the answer choices to determine which one matches the graph.

Final Answer

The final answer is Graph D.

$$

Understanding the Inequality

To graph the inequality $y - 5 \ \textgreater \ 2x - 10$, we need to first rewrite it in a more familiar form. By adding 5 to both sides, we get $y \ \textgreater \ 2x - 5$. This is a linear inequality in slope-intercept form, where the slope is 2 and the y-intercept is -5.

Graphing the Inequality

To graph the inequality, we need to first graph the corresponding equation $y = 2x - 5$. This is a line with a slope of 2 and a y-intercept of -5. We can graph this line by plotting two points on the line and drawing a line through them.

Finding the Solution Region

Since the inequality is $y \ \textgreater \ 2x - 5$, we need to find the region above the line $y = 2x - 5$. This means that any point above the line is a solution to the inequality.

Graphing the Solution Region

To graph the solution region, we can draw a dashed line to represent the boundary of the solution region. We can also shade the region above the line to indicate that it is the solution region.

Comparing with Answer Choices

Now that we have graphed the inequality, we can compare it with the answer choices to determine which one matches the graph.

Graph A

Graph A is a line with a slope of 2 and a y-intercept of -5. However, it is a solid line, which means it represents an equation, not an inequality. Therefore, Graph A does not match the graph of the inequality.

Graph B

Graph B is a line with a slope of 2 and a y-intercept of -5. However, it is a dashed line, which means it represents an inequality. However, the inequality is $y \ \textless \ 2x - 5$, not $y \ \textgreater \ 2x - 5$. Therefore, Graph B does not match the graph of the inequality.

Graph C

Graph C is a line with a slope of 2 and a y-intercept of -5. However, it is a solid line, which means it represents an equation, not an inequality. However, the inequality is $y \ \textgreater \ 2x - 5$, which is the same as the original inequality. Therefore, Graph C does not match the graph of the inequality.

Graph D

Graph D is a line with a slope of 2 and a y-intercept of -5. However, it is a dashed line, which means it represents an inequality. The inequality is $y \ \textgreater \ 2x - 5$, which is the same as the original inequality. Therefore, Graph D matches the graph of the inequality.

Q&A

Q: What is the first step in graphing the inequality $y - 5 \ \textgreater \ 2x - 10$?

A: The first step is to rewrite the inequality in a more familiar form by adding 5 to both sides: $y \ \textgreater \ 2x - 5$.

Q: What is the slope of the line $y = 2x - 5$?

A: The slope of the line $y = 2x - 5$ is 2.

Q: What is the y-intercept of the line $y = 2x - 5$?

A: The y-intercept of the line $y = 2x - 5$ is -5.

Q: What is the solution region for the inequality $y \ \textgreater \ 2x - 5$?

A: The solution region is the region above the line $y = 2x - 5$.

Q: How do you graph the solution region?

A: To graph the solution region, draw a dashed line to represent the boundary of the solution region and shade the region above the line.

Q: Which answer choice matches the graph of the inequality $y - 5 \ \textgreater \ 2x - 10$?

A: The answer choice that matches the graph of the inequality is Graph D.

Conclusion

Graphing the inequality $y - 5 \ \textgreater \ 2x - 10$ requires rewriting the inequality in a more familiar form, graphing the corresponding equation, finding the solution region, and graphing the solution region. By following these steps, we can determine which answer choice matches the graph of the inequality.

Step-by-Step Solution

Here is a step-by-step solution to the problem:

1. Rewrite the inequality in a more familiar form by adding 5 to both sides: $y \ \textgreater \ 2x - 5$.
2. Graph the corresponding equation $y = 2x - 5$ by plotting two points on the line and drawing a line through them.
3. Find the solution region by determining the region above the line $y = 2x - 5$.
4. Graph the solution region by drawing a dashed line to represent the boundary of the solution region and shading the region above the line.
5. Compare the graph with the answer choices to determine which one matches the graph.

Final Answer

The final answer is Graph D.