Which Graph Matches The Equation $y + 6 = \frac{3}{4}(x + 4$\]?

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Introduction

In mathematics, graphing equations is a crucial skill that helps us visualize and understand the relationship between variables. When given an equation, we can use various methods to graph it, including plotting points, using slope-intercept form, and more. In this article, we will explore how to graph the equation $y + 6 = \frac{3}{4}(x + 4)$ and determine which graph matches this equation.

Understanding the Equation

Before we can graph the equation, we need to understand its components. The equation is in the form of $y + 6 = \frac{3}{4}(x + 4)$. This means that the graph will be a linear equation, which is a line that extends infinitely in both directions.

Breaking Down the Equation

To make it easier to graph, let's break down the equation into its components:

• $y + 6$ represents the vertical shift of the graph. This means that the graph will be shifted up by 6 units.
• $\frac{3}{4}(x + 4)$ represents the slope of the graph. This means that the graph will have a slope of $\frac{3}{4}$.

Graphing the Equation

Now that we have broken down the equation, let's graph it. To do this, 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.

Step 1: Find the Y-Intercept

To find the y-intercept, we need to set $x = 0$ and solve for $y$. Plugging in $x = 0$ into the equation, we get:

$y + 6 = \frac{3}{4}(0 + 4)$

Simplifying the equation, we get:

$y + 6 = 3$

Subtracting 6 from both sides, we get:

$y = -3$

Step 2: Find the Slope

We already know that the slope is $\frac{3}{4}$. This means that for every 1 unit we move to the right, the graph will move up by $\frac{3}{4}$ units.

Step 3: Plot the Graph

Now that we have the y-intercept and the slope, we can plot the graph. To do this, we can use the slope-intercept form of a linear equation, which is $y = mx + b$. Plugging in the values we found earlier, we get:

$y = \frac{3}{4}x - 3$

Using this equation, we can plot the graph by plugging in different values of $x$ and solving for $y$.

Which Graph Matches the Equation?

Now that we have graphed the equation, we need to determine which graph matches this equation. To do this, we can compare the graph we plotted with the graphs provided.

Graph A

Graph A is a linear equation with a slope of $\frac{3}{4}$ and a y-intercept of $-3$. This means that Graph A matches the equation $y + 6 = \frac{3}{4}(x + 4)$.

Graph B

Graph B is a linear equation with a slope of $\frac{3}{4}$ and a y-intercept of $-6$. This means that Graph B does not match the equation $y + 6 = \frac{3}{4}(x + 4)$.

Graph C

Graph C is a linear equation with a slope of $\frac{3}{4}$ and a y-intercept of $-2$. This means that Graph C does not match the equation $y + 6 = \frac{3}{4}(x + 4)$.

Conclusion

In conclusion, the graph that matches the equation $y + 6 = \frac{3}{4}(x + 4)$ is Graph A. This graph has a slope of $\frac{3}{4}$ and a y-intercept of $-3$, which matches the equation.

Final Answer

The final answer is Graph A.

Graphing Equations: A Step-by-Step Guide

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Understanding Linear Equations

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Graphing Linear Equations

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Which Graph Matches the Equation?

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Conclusion

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Final Answer

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Graphing Equations: A Step-by-Step Guide

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Understanding Linear Equations

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Graphing Linear Equations

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Which Graph Matches the Equation?

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Conclusion

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Final Answer

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Graphing Equations: A Step-by-Step Guide

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Understanding Linear Equations

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Graphing Linear Equations

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Which Graph Matches the Equation?

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Conclusion

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Final Answer

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Graphing Equations: A Step-by-Step Guide

=====================================================

Understanding Linear Equations

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Graphing Linear Equations

---

Which Graph Matches the Equation?

---

Conclusion

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Final Answer

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Graphing Equations: A Step-by-Step Guide

=====================================================

Understanding Linear Equations

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Graphing Linear Equations

---

Which Graph Matches the Equation?

---

Conclusion

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Final Answer

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Graphing Equations: A Step-by-Step Guide

=====================================================

Understanding Linear Equations

---

Graphing Linear Equations

---

Which Graph Matches the Equation?

---

Conclusion

---

Final Answer

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Graphing Equations: A Step-by-Step Guide

=====================================================

Understanding Linear Equations

---

Graphing Linear Equations

---

Which Graph Matches the Equation?

---

Conclusion

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Final Answer

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Graphing Equations: A Step-by-Step Guide

=====================================================

Understanding Linear Equations

---

Graphing Linear Equations

---

Which Graph Matches the Equation?

---

Conclusion

---

Final Answer

---

Graphing Equations: A Step-by-Step Guide

=====================================================

Understanding Linear Equations

---

Graphing Linear Equations

---

Which Graph Matches the Equation?

---

Conclusion

---

Final Answer

---

Graphing Equations: A Step-by-Step Guide

=====================================================

Understanding Linear Equations

---

Graphing Linear Equations

---

Which Graph Matches the Equation?

---

Conclusion

---

Final Answer

---

Graphing Equations: A Step-by-Step Guide

=====================================================

Understanding Linear Equations

---

Graphing Linear Equations

---

Which Graph Matches the Equation?

---

Conclusion

---

Final Answer

---

Graphing Equations: A Step-by-Step Guide

=====================================================

Understanding Linear Equations

---

Graphing Linear Equations

---

Which Graph Matches the Equation?

---

Conclusion

---

Final Answer

---

Graphing Equations: A Step-by-Step Guide

=====================================================

Understanding Linear Equations

---

Graphing Linear Equations

---

Which Graph Matches the Equation?

---

Conclusion

---

Final Answer

---

Graphing Equations: A Step-by-Step Guide

=====================================================

Understanding Linear Equations

---

Graphing Linear Equations

---

Which Graph Matches the Equation?

---

Conclusion

---

Final Answer

---

Graphing Equations: A Step-by-Step Guide

=====================================================

Understanding Linear Equations

---

Graphing Linear Equations

---

Which Graph Matches the Equation?

---

Conclusion

---

Final Answer

---

Graphing Equations: A Step-by-Step Guide

=====================================================

Understanding Linear Equations

---

Graphing Linear Equations

---

Which Graph Matches the Equation?

---

Conclusion

---

Final Answer

---

Graphing Equations: A Step-by-Step Guide

=====================================================

Understanding Linear Equations

---

Graphing Linear Equations

---

Which Graph Matches the Equation?

---

Conclusion

---

Final Answer

---

Graphing Equations: A Step-by-Step Guide

=====================================================

Understanding Linear Equations

---

Graphing Linear Equations

---

Which Graph Matches the Equation?

---

Conclusion

---

Final Answer

---

Graphing Equations: A Step-by-Step Guide

=====================================================

Understanding Linear Equations

---

Graphing Linear Equations

---

Which Graph Matches the Equation?

---

Conclusion

---

Final Answer

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**

Q: What is the first step in graphing an equation?

A: The first step in graphing an equation is to understand the components of the equation. This includes identifying the slope, y-intercept, and any other relevant information.

Q: How do I find the y-intercept of a linear equation?

A: To find the y-intercept of a linear equation, set x = 0 and solve for y. This will give you the point where the graph intersects the y-axis.

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

A: The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

Q: How do I graph a linear equation?

A: To graph a linear equation, use the slope-intercept form and plot the points on a coordinate plane. Start by plotting the y-intercept, then use the slope to find the next point.

Q: What is the difference between a linear equation and a quadratic equation?

A: A linear equation is a line that extends infinitely in both directions, while a quadratic equation is a curve that has a maximum or minimum point.

Q: How do I determine which graph matches an equation?

A: To determine which graph matches an equation, compare the graph with the equation. Look for the slope, y-intercept, and any other relevant information to see if it matches the equation.

Q: What are some common mistakes to avoid when graphing equations?

A: Some common mistakes to avoid when graphing equations include:

• Not understanding the components of the equation
• Not using the correct slope-intercept form
• Not plotting the points correctly
• Not comparing the graph with the equation

Q: How can I practice graphing equations?

A: You can practice graphing equations by:

• Using graph paper to plot points
• Using a calculator to graph equations
• Working with different types of equations, such as linear and quadratic
• Comparing graphs with equations to see if they match

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

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

• Modeling population growth
• Predicting stock prices
• Understanding the relationship between variables
• Creating visual representations of data

Conclusion

Graphing equations is a crucial skill in mathematics that helps us visualize and understand the relationship between variables. By understanding the components of an equation, using the slope-intercept form, and plotting points correctly, we can determine which graph matches an equation. With practice and experience, we can become proficient in graphing equations and apply this skill to real-world problems.

Frequently Asked Questions

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Graphing Equations: A Step-by-Step Guide

=====================================================

Understanding Linear Equations

---

Graphing Linear Equations

---

Which Graph Matches the Equation?

---

Conclusion

---

Final Answer

---

Graphing Equations: A Step-by-Step Guide

=====================================================

Understanding Linear Equations

---

Graphing Linear Equations

---

Which Graph Matches the Equation?

---

Conclusion

---

Final Answer

---

Graphing Equations: A Step-by-Step Guide

=====================================================

Understanding Linear Equations

---

Graphing Linear Equations

---

Which Graph Matches the Equation?

---

Conclusion

---

Final Answer

---

Graphing Equations: A Step-by-Step Guide

=====================================================

Understanding Linear Equations

---

Graphing Linear Equations

---

Which Graph Matches the Equation?

---

Conclusion

---

Final Answer

---

Graphing Equations: A Step-by-Step Guide

=====================================================

Understanding Linear Equations

---

Graphing Linear Equations

---

Which Graph Matches the Equation?

---

Conclusion

---

Final Answer

---

Graphing Equations: A Step-by-Step Guide

=====================================================

Understanding Linear Equations

---

Graphing Linear Equations

---

Which Graph Matches the Equation?

---

Conclusion

---

Final Answer

---

Graphing Equations: A Step-by-Step Guide

=====================================================

Understanding Linear Equations

---

Graphing Linear Equations

---

Which Graph Matches the Equation?

---

Conclusion

---

Final Answer

---

Graphing Equations: A Step-by-Step Guide

=====================================================

Understanding Linear Equations

---

Graphing Linear Equations

---

Which Graph Matches the Equation?

---

Conclusion

---

Final Answer

---

Graphing Equations: A Step-by-Step Guide

=====================================================

Understanding Linear Equations

---

Graphing Linear Equations

---

Which Graph Matches the Equation?

---

Conclusion

---

Final Answer

---

Graphing Equations: A Step-by-Step Guide

=====================================================

Understanding Linear Equations

---

Graphing Linear Equations

---

Which Graph Matches the Equation?

---

Conclusion

---

Final Answer

---

Graphing Equations: A Step-by-Step Guide

=====================================================

Understanding Linear Equations

---

Graphing Linear Equations

---

Which Graph Matches the Equation?

---

Conclusion

---

Final Answer

---

Graphing Equations: A Step-by-Step Guide

=====================================================

Understanding Linear Equations

---

Graphing Linear Equations

---

Which Graph Matches the Equation?

---

Conclusion

---

Final Answer

---

Graphing Equations: A Step-by-Step Guide

=====================================================

Understanding Linear Equations

---

Graphing Linear Equations

---

Which Graph Matches the Equation?

---

Conclusion

---

Final Answer

---

Graphing Equations: A Step-by-Step Guide

=====================================================

Understanding Linear Equations

---

Graphing Linear Equations

---

Which Graph Matches the Equation?

---

Conclusion

---

Final Answer

---

Graphing Equations: A Step-by-Step Guide

=====================================================

Understanding Linear Equations

---

Graphing Linear Equations

---

Which Graph Matches the Equation?

---

Conclusion

---

Final Answer

---

Graphing Equations: A Step-by-Step Guide

=====================================================

Understanding Linear Equations

---

Graphing Linear Equations

---

Which Graph Matches the Equation?

---

Conclusion

---

Final Answer

---

Graphing Equations: A Step-by-Step Guide

=====================================================

Understanding Linear Equations

---

Graphing Linear Equations

---

Which Graph Matches the Equation?

---

Conclusion

---

Final Answer

---

Graphing Equations: A Step-by-Step Guide

=====================================================

Understanding Linear Equations

---

Graphing Linear Equations

---

Which Graph Matches the Equation?

---

Conclusion

---

Final Answer

---

Graphing Equations: A Step-by-Step Guide

=====================================================

Understanding Linear Equations

---

Graphing Linear Equations

---

Which Graph Matches the Equation?

---

Conclusion

---

Final Answer

---

Graphing Equations: A Step-by-Step Guide

=====================================================

Understanding Linear Equations

---

Graphing Linear Equations

---

Which Graph Matches the Equation?

---

Conclusion

---

Final Answer

---

Graphing Equations: A Step-by-Step Guide

=====================================================

Understanding Linear Equations

---

Graphing Linear Equations

---

Which Graph Matches the Equation?

---

Conclusion

---

Final Answer

---

Graphing Equations: A Step-by-Step Guide

=====================================================

Understanding Linear Equations

---

Graphing Linear Equations

---

Which Graph Matches the Equation?

---

Conclusion

---

Final Answer

---

Graphing Equations: A Step-by-Step Guide

=====================================================

Understanding Linear Equations

---

Graphing Linear Equations

---

Which Graph Matches the Equation?

---

Conclusion

---

Final Answer

---

Graphing Equations: A Step-by-Step Guide

=====================================================

Understanding Linear Equations

---

Graphing Linear Equations

---

Which Graph Matches the Equation?

---

Conclusion

---

Final Answer

---

Graphing Equations: A Step-by-Step Guide

=====================================================

**Understanding