Which Is The Graph Of $4x - 3y = 12$?

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Introduction to Graphing Linear Equations

Graphing linear equations is a fundamental concept in mathematics, and it plays a crucial role in various fields such as physics, engineering, and computer science. A linear equation is an equation in which the highest power of the variable(s) is 1. In this article, we will focus on graphing the linear equation $4x - 3y = 12$. We will explore the concept of graphing linear equations, understand the equation $4x - 3y = 12$, and determine its graph.

Understanding the Equation $4x - 3y = 12$

The equation $4x - 3y = 12$ is a linear equation in two variables, $x$ and $y$. To graph this equation, we need to understand its components. The equation can be rewritten in the slope-intercept form, $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

To rewrite the equation in slope-intercept form, we need to isolate $y$ on one side of the equation. We can do this by subtracting $4x$ from both sides of the equation and then dividing both sides by $-3$.

$$4x - 3y = 12$$

$$-3y = -4x + 12$$

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

Now that we have rewritten the equation in slope-intercept form, we can see that the slope, $m$, is $\frac{4}{3}$ and the y-intercept, $b$, is $-4$.

Graphing the Equation $4x - 3y = 12$

To graph the equation $4x - 3y = 12$, we can use the slope-intercept form, $y = mx + b$. We know that the slope, $m$, is $\frac{4}{3}$ and the y-intercept, $b$, is $-4$. We can plot the y-intercept, which is the point where the graph intersects the y-axis. The y-intercept is $(-4, 0)$.

Next, we can use the slope to find another point on the graph. The slope, $\frac{4}{3}$, represents the rate of change of the graph. We can choose a point on the x-axis, say $x = 3$, and find the corresponding value of $y$ using the slope-intercept form.

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

$$y = \frac{4}{3}(3) - 4$$

$$y = 4 - 4$$

$$y = 0$$

So, the point $(3, 0)$ is on the graph.

Determining the Graph of the Equation $4x - 3y = 12$

Now that we have plotted the y-intercept and another point on the graph, we can determine the graph of the equation $4x - 3y = 12$. The graph is a straight line that passes through the points $(-4, 0)$ and $(3, 0)$. The slope of the graph is $\frac{4}{3}$, which represents the rate of change of the graph.

Conclusion

In this article, we have explored the concept of graphing linear equations and determined the graph of the equation $4x - 3y = 12$. We have rewritten the equation in slope-intercept form, $y = mx + b$, and used the slope and y-intercept to plot the graph. The graph is a straight line that passes through the points $(-4, 0)$ and $(3, 0)$. The slope of the graph is $\frac{4}{3}$, which represents the rate of change of the graph.

Final Thoughts

Graphing linear equations is a fundamental concept in mathematics, and it plays a crucial role in various fields such as physics, engineering, and computer science. In this article, we have determined the graph of the equation $4x - 3y = 12$ and explored the concept of graphing linear equations. We hope that this article has provided valuable insights into the concept of graphing linear equations and has helped readers to understand the graph of the equation $4x - 3y = 12$.

References

• [1] "Graphing Linear Equations" by Math Open Reference
• [2] "Linear Equations" by Khan Academy
• [3] "Graphing Linear Equations" by Purplemath

Glossary

• Linear Equation: An equation in which the highest power of the variable(s) is 1.
• Slope-Intercept Form: A form of a linear equation, $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.
• Graph: A visual representation of a linear equation.
• Slope: The rate of change of a graph.
• Y-Intercept: The point where a graph intersects the y-axis.
  

Introduction

Graphing linear equations is a fundamental concept in mathematics, and it plays a crucial role in various fields such as physics, engineering, and computer science. In this article, we will answer some frequently asked questions about graphing linear equations, including the equation $4x - 3y = 12$.

Q: What is the graph of the equation $4x - 3y = 12$?

A: The graph of the equation $4x - 3y = 12$ is a straight line that passes through the points $(-4, 0)$ and $(3, 0)$. The slope of the graph is $\frac{4}{3}$, which represents the rate of change of the graph.

Q: How do I graph a linear equation?

A: To graph a linear equation, you need to rewrite it in slope-intercept form, $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. Then, you can plot the y-intercept and use the slope to find another point on the graph.

Q: What is the slope of a linear equation?

A: The slope of a linear equation is the rate of change of the graph. It represents how much the graph changes for a one-unit change in the x-coordinate.

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

A: To find the y-intercept of a linear equation, you need to rewrite it in slope-intercept form, $y = mx + b$. The y-intercept is the value of $b$.

Q: Can I graph a linear equation by hand?

A: Yes, you can graph a linear equation by hand. However, it can be time-consuming and may not be as accurate as using a graphing calculator or computer software.

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

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

• Not rewriting the equation in slope-intercept form
• Not plotting the y-intercept
• Not using the slope to find another point on the graph
• Not checking the graph for accuracy

Q: How do I check the accuracy of a graph?

A: To check the accuracy of a graph, you can use a graphing calculator or computer software to plot the graph and compare it to your hand-drawn graph.

Q: Can I graph non-linear equations?

A: Yes, you can graph non-linear equations. However, non-linear equations are more complex and may require the use of advanced mathematical techniques and software.

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

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

• Physics: Graphing linear equations is used to model the motion of objects and predict their trajectories.
• Engineering: Graphing linear equations is used to design and optimize systems, such as bridges and buildings.
• Computer Science: Graphing linear equations is used to develop algorithms and models for computer graphics and game development.

Conclusion

In this article, we have answered some frequently asked questions about graphing linear equations, including the equation $4x - 3y = 12$. We hope that this article has provided valuable insights into the concept of graphing linear equations and has helped readers to understand the graph of the equation $4x - 3y = 12$.

Final Thoughts

Graphing linear equations is a fundamental concept in mathematics, and it plays a crucial role in various fields such as physics, engineering, and computer science. In this article, we have explored the concept of graphing linear equations and have answered some frequently asked questions. We hope that this article has provided valuable insights into the concept of graphing linear equations and has helped readers to understand the graph of the equation $4x - 3y = 12$.

References

• [1] "Graphing Linear Equations" by Math Open Reference
• [2] "Linear Equations" by Khan Academy
• [3] "Graphing Linear Equations" by Purplemath

Glossary

• Linear Equation: An equation in which the highest power of the variable(s) is 1.
• Slope-Intercept Form: A form of a linear equation, $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.
• Graph: A visual representation of a linear equation.
• Slope: The rate of change of a graph.
• Y-Intercept: The point where a graph intersects the y-axis.