Graph The Line: 3x + Y = 9 Explanation: [Provide An Explanation Of How To Graph The Line, If Necessary.]Check: [Provide Steps Or Methods To Verify The Accuracy Of The Graph, If Necessary.]

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Introduction

Graphing a line is an essential skill in mathematics, particularly in algebra and geometry. It involves representing a linear equation on a coordinate plane, which helps us visualize the relationship between the variables. In this article, we will focus on graphing the line represented by the equation 3x + y = 9.

Understanding the Equation

Before we dive into graphing, let's break down the equation 3x + y = 9. This is a linear equation in two variables, x and y. The equation is in the form of Ax + By = C, where A, B, and C are constants. In this case, A = 3, B = 1, and C = 9.

Graphing the Line

To graph the line, we need to find two points on the line. We can do this by substituting different values of x into the equation and solving for y. Let's start by finding the y-intercept, which is the point where the line intersects the y-axis.

Finding the y-Intercept

To find the y-intercept, we set x = 0 and solve for y.

3(0) + y = 9 y = 9

So, the y-intercept is (0, 9).

Finding the x-Intercept

To find the x-intercept, we set y = 0 and solve for x.

3x + 0 = 9 3x = 9 x = 3

So, the x-intercept is (3, 0).

Plotting the Points

Now that we have the y-intercept and x-intercept, we can plot these points on the coordinate plane.

  • The y-intercept is (0, 9), which means it lies on the y-axis at a distance of 9 units from the origin.
  • The x-intercept is (3, 0), which means it lies on the x-axis at a distance of 3 units from the origin.

Drawing the Line

With the two points plotted, we can draw a line that passes through them. Since the line is straight, we can use a ruler or a straightedge to draw it.

Checking the Graph

To verify the accuracy of the graph, we can use the following methods:

Checking the y-Intercept

We can check the y-intercept by substituting x = 0 into the equation.

3(0) + y = 9 y = 9

This confirms that the y-intercept is indeed (0, 9).

Checking the x-Intercept

We can check the x-intercept by substituting y = 0 into the equation.

3x + 0 = 9 3x = 9 x = 3

This confirms that the x-intercept is indeed (3, 0).

Checking the Line

We can check the line by substituting different values of x into the equation and solving for y. Let's try x = 1.

3(1) + y = 9 3 + y = 9 y = 6

This confirms that the point (1, 6) lies on the line.

Conclusion

Graphing the line 3x + y = 9 involves finding the y-intercept and x-intercept, plotting the points, and drawing a line that passes through them. We can verify the accuracy of the graph by checking the y-intercept, x-intercept, and the line itself. By following these steps, we can create an accurate graph of the line.

Discussion

Graphing lines is an essential skill in mathematics, particularly in algebra and geometry. It helps us visualize the relationship between the variables and understand the behavior of the line. In this article, we focused on graphing the line 3x + y = 9, but the same principles can be applied to graphing other lines.

Common Mistakes

When graphing lines, it's essential to avoid common mistakes such as:

  • Incorrect y-intercept: Make sure to set x = 0 and solve for y correctly.
  • Incorrect x-intercept: Make sure to set y = 0 and solve for x correctly.
  • Incorrect line: Make sure to plot the points correctly and draw a line that passes through them.

Real-World Applications

Graphing lines has numerous real-world applications, such as:

  • Physics: Graphing lines is essential in physics to represent the motion of objects and understand the relationship between variables.
  • Engineering: Graphing lines is used in engineering to design and optimize systems, such as electrical circuits and mechanical systems.
  • Economics: Graphing lines is used in economics to represent the relationship between variables, such as supply and demand.

Conclusion

Introduction

Graphing a line is an essential skill in mathematics, particularly in algebra and geometry. In our previous article, we explained how to graph the line represented by the equation 3x + y = 9. In this article, we will answer some frequently asked questions about graphing lines.

Q&A

Q: What is the y-intercept of the line 3x + y = 9?

A: The y-intercept of the line 3x + y = 9 is (0, 9). To find the y-intercept, we set x = 0 and solve for y.

Q: What is the x-intercept of the line 3x + y = 9?

A: The x-intercept of the line 3x + y = 9 is (3, 0). To find the x-intercept, we set y = 0 and solve for x.

Q: How do I graph a line if I don't have a calculator?

A: You can graph a line without a calculator by using a ruler or a straightedge to draw a line that passes through the y-intercept and x-intercept.

Q: Can I graph a line if I only have the equation in slope-intercept form?

A: Yes, you can graph a line if you only have the equation in slope-intercept form. The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

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

A: You can check the accuracy of your graph by substituting different values of x into the equation and solving for y. You can also check the y-intercept and x-intercept to make sure they are correct.

Q: Can I graph a line if I have a system of equations?

A: Yes, you can graph a line if you have a system of equations. You can solve the system of equations to find the y-intercept and x-intercept, and then graph the line.

Q: How do I graph a line if I have a quadratic equation?

A: You can graph a line if you have a quadratic equation by first finding the x-intercepts and then drawing a line that passes through them.

Q: Can I graph a line if I have a rational equation?

A: Yes, you can graph a line if you have a rational equation by first finding the x-intercepts and then drawing a line that passes through them.

Q: How do I graph a line if I have a polynomial equation?

A: You can graph a line if you have a polynomial equation by first finding the x-intercepts and then drawing a line that passes through them.

Conclusion

Graphing lines is an essential skill in mathematics, particularly in algebra and geometry. In this article, we answered some frequently asked questions about graphing lines. By following these steps, you can create an accurate graph of a line.

Common Mistakes

When graphing lines, it's essential to avoid common mistakes such as:

  • Incorrect y-intercept: Make sure to set x = 0 and solve for y correctly.
  • Incorrect x-intercept: Make sure to set y = 0 and solve for x correctly.
  • Incorrect line: Make sure to plot the points correctly and draw a line that passes through them.

Real-World Applications

Graphing lines has numerous real-world applications, such as:

  • Physics: Graphing lines is essential in physics to represent the motion of objects and understand the relationship between variables.
  • Engineering: Graphing lines is used in engineering to design and optimize systems, such as electrical circuits and mechanical systems.
  • Economics: Graphing lines is used in economics to represent the relationship between variables, such as supply and demand.

Conclusion

Graphing the line 3x + y = 9 involves finding the y-intercept and x-intercept, plotting the points, and drawing a line that passes through them. We can verify the accuracy of the graph by checking the y-intercept, x-intercept, and the line itself. By following these steps, we can create an accurate graph of the line.