Finding X And Y Intercepts Worksheet Day 1 Answer Key
Table of Contents :
Finding the X and Y intercepts of a function is an essential skill in algebra that helps in graphing linear equations and understanding their behavior. This article will explore the concept of intercepts, how to find them, and will provide a detailed answer key for a worksheet designed for practice.
Understanding X and Y Intercepts
What are Intercepts?
Intercepts refer to the points where a graph crosses the axes on a coordinate plane. The X-intercept is where the graph crosses the x-axis (where y = 0), and the Y-intercept is where it crosses the y-axis (where x = 0).
Importance of Finding Intercepts
Finding intercepts is crucial for graphing linear equations. By knowing where a line crosses the axes, students can sketch the graph more accurately without plotting numerous points. Understanding intercepts also helps in analyzing the behavior of equations in real-world scenarios, such as determining break-even points in business.
How to Find X and Y Intercepts
Finding the X-Intercept
To find the X-intercept of a function, follow these steps:
- Set ( y = 0 ) in the equation.
- Solve for ( x ).
Example: For the equation ( 2x + 3y = 6 ):
- Set ( y = 0 ):
- ( 2x + 3(0) = 6 )
- ( 2x = 6 )
- ( x = 3 )
- So, the X-intercept is (3, 0).
Finding the Y-Intercept
To find the Y-intercept, follow these steps:
- Set ( x = 0 ) in the equation.
- Solve for ( y ).
Example: For the same equation ( 2x + 3y = 6 ):
- Set ( x = 0 ):
- ( 2(0) + 3y = 6 )
- ( 3y = 6 )
- ( y = 2 )
- Thus, the Y-intercept is (0, 2).
Sample Worksheet: Finding X and Y Intercepts
To practice finding intercepts, here is a worksheet you can work on, followed by an answer key. The worksheet consists of five linear equations:
- ( x + 2y = 4 )
- ( 3x - y = 5 )
- ( 4x + 5y = 20 )
- ( 2x - 3y = 6 )
- ( 5x + 2y = 10 )
Answer Key for Finding X and Y Intercepts
| Equation | X-Intercept | Y-Intercept |
|---|---|---|
| ( x + 2y = 4 ) | (4, 0) | (0, 2) |
| ( 3x - y = 5 ) | (5/3, 0) | (0, -5) |
| ( 4x + 5y = 20 ) | (5, 0) | (0, 4) |
| ( 2x - 3y = 6 ) | (3, 0) | (0, -2) |
| ( 5x + 2y = 10 ) | (2, 0) | (0, 5) |
Detailed Solutions
-
Equation: ( x + 2y = 4 )
- X-intercept: Set ( y = 0 ) ➔ ( x + 2(0) = 4 ) ➔ ( x = 4 ) ➔ ( (4, 0) )
- Y-intercept: Set ( x = 0 ) ➔ ( 0 + 2y = 4 ) ➔ ( y = 2 ) ➔ ( (0, 2) )
-
Equation: ( 3x - y = 5 )
- X-intercept: Set ( y = 0 ) ➔ ( 3x - 0 = 5 ) ➔ ( x = \frac{5}{3} ) ➔ ( (5/3, 0) )
- Y-intercept: Set ( x = 0 ) ➔ ( 0 - y = 5 ) ➔ ( y = -5 ) ➔ ( (0, -5) )
-
Equation: ( 4x + 5y = 20 )
- X-intercept: Set ( y = 0 ) ➔ ( 4x = 20 ) ➔ ( x = 5 ) ➔ ( (5, 0) )
- Y-intercept: Set ( x = 0 ) ➔ ( 5y = 20 ) ➔ ( y = 4 ) ➔ ( (0, 4) )
-
Equation: ( 2x - 3y = 6 )
- X-intercept: Set ( y = 0 ) ➔ ( 2x = 6 ) ➔ ( x = 3 ) ➔ ( (3, 0) )
- Y-intercept: Set ( x = 0 ) ➔ ( -3y = 6 ) ➔ ( y = -2 ) ➔ ( (0, -2) )
-
Equation: ( 5x + 2y = 10 )
- X-intercept: Set ( y = 0 ) ➔ ( 5x = 10 ) ➔ ( x = 2 ) ➔ ( (2, 0) )
- Y-intercept: Set ( x = 0 ) ➔ ( 2y = 10 ) ➔ ( y = 5 ) ➔ ( (0, 5) )
Important Notes
"Understanding how to find the intercepts not only aids in graphing but also strengthens problem-solving skills in mathematics. Practice is key, and worksheets can help reinforce these concepts."
Conclusion
Learning to find x and y intercepts is foundational for mastering linear equations. By practicing with worksheets and using the answer keys provided, students can improve their skills and confidence in algebra. With time and practice, finding intercepts will become a quick and straightforward task!