INTERCEPT
Definition OfIntercept
The point at which a curve intersects an axis is known as an Intercept
More About Intercept
The x-intercept is the point where the curve crosses the x-axis and the y-intercept is the point where the curve crosses the y-axis.
Video Examples: X and Y intercepts
Example of Intercept
In the figure, the line cuts the x-axis at (- 2, 0) and y-axis at (0, - 3). So, x-intercept is - 2 and y-intercept is - 3.
Solved Example on Intercept
Ques: Find the x and y intercepts of the line AB shown below.
Choices:
A. x-intercept is - 3 and y-intercept is 0
B. x-intercept is 3 and y-intercept is - 3
C. x-intercept is - 3 and y-intercept is 3
D. x-intercept is 3 and y-intercept is 3
Correct Answer: C
Solution:
Step 1: The x-intercept is the x-coordinate of the point where a line crosses the x-axis.
Step 2: In the figure, the line crosses the x-axis at B (- 3, 0).
Step 3: So, the x-intercept of the line is - 3.
Step 4: The y-intercept is the y-coordinate of the point where a line crosses the y-axis.
Step 5: In the figure, the line crosses the y-axis at A (0, 3).
Step 6: So, the y-intercept of the line is 3.
Step 7: The x and y-intercepts of the line are - 3 and 3 respectively.
Quick Summary
- The x-intercept is the x-coordinate where the line crosses the x-axis (y=0).
- The y-intercept is the y-coordinate where the line crosses the y-axis (x=0).
⚠️ Common Mistakes
- Confusing x and y intercepts.
- Incorrectly solving for the intercept values from a given equation.
- Forgetting that the intercept is a point, not just a number
📋 Standards Alignment
CCSS.MATH.CONTENT.HSG.GPE.A.2CCSS.MATH.CONTENT.HSF.IF.C.7a
🍎 Teacher Insights
Use graphical representations to visually demonstrate intercepts. Emphasize the relationship between intercepts and real-world scenarios.🎓 Prerequisites
- Basic Algebra
- Coordinate Plane
- Linear Equations
Check Your Knowledge
Q1: What is the y-intercept of the line y = 2x + 3?
Q2: What is the x-intercept of the line y = x - 5?
Frequently Asked Questions
Q: How do I find the x-intercept?
A: Set y = 0 in the equation and solve for x.
Q: How do I find the y-intercept?
A: Set x = 0 in the equation and solve for y.