Select The Correct Answer From Each Drop-down Menu.The Equation Of A Line Is $\frac{2}{5} X+\frac{1}{10} Y=2$.The $x$-intercept Of The Line Is $\square$, And Its $y$-intercept Is $\square$.

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Understanding the Equation of a Line

The equation of a line is given by 25x+110y=2\frac{2}{5} x+\frac{1}{10} y=2. To find the x-intercept and y-intercept of the line, we need to understand the concept of intercepts and how to find them from the equation of a line.

What are X and Y Intercepts?

The x-intercept of a line is the point where the line intersects the x-axis. At this point, the value of y is always 0. Similarly, the y-intercept of a line is the point where the line intersects the y-axis. At this point, the value of x is always 0.

Finding the X-Intercept

To find the x-intercept of the line, we need to substitute y = 0 into the equation of the line. This will give us the value of x at the x-intercept.

Let's substitute y = 0 into the equation of the line:

25x+110(0)=2\frac{2}{5} x+\frac{1}{10} (0)=2

Simplifying the equation, we get:

25x=2\frac{2}{5} x=2

Multiplying both sides of the equation by 5, we get:

2x=102x=10

Dividing both sides of the equation by 2, we get:

x=5x=5

Therefore, the x-intercept of the line is 5.

Finding the Y-Intercept

To find the y-intercept of the line, we need to substitute x = 0 into the equation of the line. This will give us the value of y at the y-intercept.

Let's substitute x = 0 into the equation of the line:

25(0)+110y=2\frac{2}{5} (0)+\frac{1}{10} y=2

Simplifying the equation, we get:

110y=2\frac{1}{10} y=2

Multiplying both sides of the equation by 10, we get:

y=20y=20

Therefore, the y-intercept of the line is 20.

Conclusion

In this article, we learned how to find the x-intercept and y-intercept of a line from its equation. We used the concept of intercepts and substituted the values of x and y into the equation of the line to find the intercepts. We found that the x-intercept of the line is 5 and the y-intercept is 20.

Key Takeaways

  • The x-intercept of a line is the point where the line intersects the x-axis.
  • The y-intercept of a line is the point where the line intersects the y-axis.
  • To find the x-intercept, substitute y = 0 into the equation of the line.
  • To find the y-intercept, substitute x = 0 into the equation of the line.

Practice Problems

  1. Find the x-intercept and y-intercept of the line given by the equation x+2y=6x+2y=6.
  2. Find the x-intercept and y-intercept of the line given by the equation 2x−3y=92x-3y=9.

Answer Key

  1. x-intercept: 6, y-intercept: 3
  2. x-intercept: 4.5, y-intercept: -1.5
    Frequently Asked Questions (FAQs) about X and Y Intercepts ================================================================

Q: What is the x-intercept of a line?

A: The x-intercept of a line is the point where the line intersects the x-axis. At this point, the value of y is always 0.

Q: What is the y-intercept of a line?

A: The y-intercept of a line is the point where the line intersects the y-axis. At this point, the value of x is always 0.

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

A: To find the x-intercept of a line, substitute y = 0 into the equation of the line. This will give you the value of x at the x-intercept.

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

A: To find the y-intercept of a line, substitute x = 0 into the equation of the line. This will give you the value of y at the y-intercept.

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

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

Q: How do I find the slope of a line?

A: To find the slope of a line, use the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.

Q: Can a line have more than one x-intercept or y-intercept?

A: No, a line can only have one x-intercept and one y-intercept.

Q: What is the significance of x and y intercepts in real-life applications?

A: X and y intercepts are important in real-life applications such as physics, engineering, and economics. They help us understand the behavior of objects and systems in different situations.

Q: How do I graph a line using its x and y intercepts?

A: To graph a line using its x and y intercepts, plot the x-intercept and y-intercept on a coordinate plane and draw a line through them.

Q: Can I find the x and y intercepts of a line using a graphing calculator?

A: Yes, you can find the x and y intercepts of a line using a graphing calculator. Simply enter the equation of the line and use the calculator's built-in functions to find the intercepts.

Q: What are some common mistakes to avoid when finding x and y intercepts?

A: Some common mistakes to avoid when finding x and y intercepts include:

  • Not substituting the correct values into the equation of the line
  • Not simplifying the equation correctly
  • Not using the correct formula to find the slope of the line
  • Not plotting the x and y intercepts correctly on a coordinate plane

Conclusion

In this article, we answered some frequently asked questions about x and y intercepts. We covered topics such as the definition of x and y intercepts, how to find them, and their significance in real-life applications. We also provided some common mistakes to avoid when finding x and y intercepts.