Find The X X X -intercept And Y Y Y -intercept Of The Line. X + 2 Y = 8 X + 2y = 8 X + 2 Y = 8 X X X -intercept: □ \square □ Y Y Y -intercept: □ \square □

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Introduction

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In mathematics, the $x$-intercept and $y$-intercept of a line are two important concepts that help us understand the behavior of a line on a coordinate plane. The $x$-intercept is the point where the line crosses the $x$-axis, while the $y$-intercept is the point where the line crosses the $y$-axis. In this article, we will learn how to find the $x$-intercept and $y$-intercept of a line using a simple equation.

What are $x$-intercept and $y$-intercept?

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The $x$-intercept of a line is the point where the line crosses the $x$-axis. At this point, the value of $y$ is always zero. On the other hand, the $y$-intercept of a line is the point where the line crosses the $y$-axis. At this point, the value of $x$ is always zero.

Finding the $x$-intercept

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To find the $x$-intercept of a line, we need to set the value of $y$ to zero in the equation of the line. Let's consider the equation of the line $x + 2y = 8$. To find the $x$-intercept, we set $y$ to zero and solve for $x$.

Step 1: Set $y$ to zero

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We start by setting $y$ to zero in the equation of the line.

$x + 2(0) = 8$

Step 2: Simplify the equation

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Now, we simplify the equation by removing the zero term.

$x = 8$

Step 3: Write the $x$-intercept

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The $x$-intercept is the point where the line crosses the $x$-axis. Since the value of $y$ is always zero at this point, we can write the $x$-intercept as $(x, 0)$.

$x$-intercept: $(8, 0)$

Finding the $y$-intercept

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To find the $y$-intercept of a line, we need to set the value of $x$ to zero in the equation of the line. Let's consider the equation of the line $x + 2y = 8$. To find the $y$-intercept, we set $x$ to zero and solve for $y$.

Step 1: Set $x$ to zero

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We start by setting $x$ to zero in the equation of the line.

$0 + 2y = 8$

Step 2: Simplify the equation

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Now, we simplify the equation by removing the zero term.

$2y = 8$

Step 3: Solve for $y$

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To solve for $y$, we divide both sides of the equation by 2.

$y = \frac{8}{2}$

$y = 4$

Step 4: Write the $y$-intercept

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The $y$-intercept is the point where the line crosses the $y$-axis. Since the value of $x$ is always zero at this point, we can write the $y$-intercept as $(0, y)$.

$y$-intercept: $(0, 4)$

Conclusion

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In this article, we learned how to find the $x$-intercept and $y$-intercept of a line using a simple equation. We started by setting the value of $y$ to zero to find the $x$-intercept and the value of $x$ to zero to find the $y$-intercept. We then solved for the unknown variable and wrote the intercept as a point on the coordinate plane. By following these steps, we can easily find the $x$-intercept and $y$-intercept of any line.

Example Problems

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Problem 1

Find the $x$-intercept and $y$-intercept of the line $x + 3y = 12$.

Solution

To find the $x$-intercept, we set $y$ to zero and solve for $x$.

$x + 3(0) = 12$

$x = 12$

$x$-intercept: $(12, 0)$

To find the $y$-intercept, we set $x$ to zero and solve for $y$.

$0 + 3y = 12$

$3y = 12$

$y = \frac{12}{3}$

$y = 4$

$y$-intercept: $(0, 4)$

Problem 2

Find the $x$-intercept and $y$-intercept of the line $2x + 4y = 16$.

Solution

To find the $x$-intercept, we set $y$ to zero and solve for $x$.

$2x + 4(0) = 16$

$2x = 16$

$x = \frac{16}{2}$

$x = 8$

$x$-intercept: $(8, 0)$

To find the $y$-intercept, we set $x$ to zero and solve for $y$.

$2(0) + 4y = 16$

$4y = 16$

$y = \frac{16}{4}$

$y = 4$

$y$-intercept: $(0, 4)$

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Introduction

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In our previous article, we learned how to find the $x$-intercept and $y$-intercept of a line using a simple equation. However, we understand that there may be some questions and doubts that you may have. In this article, we will address some of the frequently asked questions about $x$-intercept and $y$-intercept.

Q&A

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Q: What is the difference between $x$-intercept and $y$-intercept?

A: The $x$-intercept is the point where the line crosses the $x$-axis, while the $y$-intercept is the point where the line crosses the $y$-axis.

Q: How do I find the $x$-intercept of a line?

A: To find the $x$-intercept, you need to set the value of $y$ to zero in the equation of the line and solve for $x$.

Q: How do I find the $y$-intercept of a line?

A: To find the $y$-intercept, you need to set the value of $x$ to zero in the equation of the line and solve for $y$.

Q: What if the equation of the line is not in the form $y = mx + b$?

A: You can still find the $x$-intercept and $y$-intercept by setting the value of $y$ to zero and solving for $x$, or setting the value of $x$ to zero and solving for $y$.

Q: Can I find the $x$-intercept and $y$-intercept of a line using a graph?

A: Yes, you can find the $x$-intercept and $y$-intercept of a line by graphing the line and finding the point where it crosses the $x$-axis and $y$-axis.

Q: What if the line does not cross the $x$-axis or $y$-axis?

A: If the line does not cross the $x$-axis or $y$-axis, then it does not have an $x$-intercept or $y$-intercept.

Q: Can I find the $x$-intercept and $y$-intercept of a line using a calculator?

A: Yes, you can find the $x$-intercept and $y$-intercept of a line using a calculator by graphing the line and finding the point where it crosses the $x$-axis and $y$-axis.

Example Problems

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Problem 1

Find the $x$-intercept and $y$-intercept of the line $x + 2y = 8$ using a graph.

Solution

To find the $x$-intercept, we graph the line and find the point where it crosses the $x$-axis.

$x$-intercept: $(8, 0)$

To find the $y$-intercept, we graph the line and find the point where it crosses the $y$-axis.

$y$-intercept: $(0, 4)$

Problem 2

Find the $x$-intercept and $y$-intercept of the line $2x + 4y = 16$ using a calculator.

Solution

To find the $x$-intercept, we graph the line using a calculator and find the point where it crosses the $x$-axis.

$x$-intercept: $(8, 0)$

To find the $y$-intercept, we graph the line using a calculator and find the point where it crosses the $y$-axis.

$y$-intercept: $(0, 4)$

Conclusion

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In this article, we addressed some of the frequently asked questions about $x$-intercept and $y$-intercept. We provided examples and solutions to help you understand the concepts better. By following the steps and using the examples, you can find the $x$-intercept and $y$-intercept of any line.

Additional Resources

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• Mathway: $x$-intercept and $y$-intercept
• Khan Academy: $x$-intercept and $y$-intercept
• Wolfram Alpha: $x$-intercept and $y$-intercept