X INTERCEPT
Definition Of X-Intercept
The x-intercept of a line is the point at which the line crosses the x-axis.
More About X-Intercept
The y-coordinate of the point where a line intersects the x-axis is 0
So, the x-intercept of a line can also be found by substituting y = 0 in the equation of the line.
Examples of X-Intercept
As the line shown in the graph is intersecting the x-axis at the point (-3, 0), so the x-intercept of the line is -3.
Video Examples: Finding the X Intercept
Solved Example on X-Intercept
Ques: Find the x-intercept of the graph of 4x + 8y = 40.
Choices:
A. - 5
B. 10
C. 5
D. - 10
Correct Answer: B
Solution:
Step 1: The x-intercept of a line is the point at which the line crosses the x-axis
Step 2: Substitute y = 0 in the given equation to find the x-intercept of the graph of the equation
Step 3: 4x + 8(0) = 40 gives x = 10
Quick Summary
- The x-intercept is the point where a line crosses the x-axis.
- At the x-intercept, the y-coordinate is always 0.
- To find the x-intercept, substitute y = 0 into the equation of the line and solve for x.
⚠️ Common Mistakes
- Confusing x-intercept with y-intercept.
- Forgetting to set y=0 when solving for the x-intercept.
- Incorrectly solving the equation after substituting y=0.
🌍 Real-World Uses
- Determining the break-even point for a business where the x-axis represents quantity sold and the y-axis represents profit/loss. The x-intercept indicates the quantity needed to sell to reach zero profit/loss.
- Calculating the time it takes for a projectile to hit the ground. The x-axis represents time, the y-axis represents height, and the x-intercept is the time when the height is zero (ground level).
- Analyzing population decline where the x-axis represents time and the y-axis represents population size. The x-intercept represents the time when the population theoretically reaches zero.
📋 Standards Alignment
CCSS.MATH.CONTENT.HSA.REI.C.6CCSS.MATH.CONTENT.HSA.REI.D.10
🔗 Related Links
🍎 Teacher Insights
Emphasize the concept that the x-intercept is a point where the line crosses the x-axis. Use graphical examples to illustrate the x-intercept. Provide practice problems with varying linear equations to reinforce the algebraic skills needed.🎓 Prerequisites
- Basic Algebra
- Coordinate Plane
- Linear Equations
Check Your Knowledge
Q1: What is the x-intercept of the line 2x + y = 4?
Q2: The x-intercept of a line is the point where the line crosses which axis?
Frequently Asked Questions
Q: What is the y-coordinate at the x-intercept?
A: The y-coordinate at the x-intercept is always 0.
Q: How do I find the x-intercept of a line?
A: Substitute y = 0 into the equation of the line and solve for x. The resulting x value is the x-intercept.