Y INTERCEPT

Y-Intercept

Definition Of Y-Intercept

The y-coordinate of the point where a line intersects the y-axis is the y-intercept of that line.

More About Y-Intercept

The x-coordinate of the point where a line intersects the y-axis is 0. So, the y-intercept of a line can also be found by substituting x = 0 in the equation of the line.

Examples of Y-Intercept

Examples of y-intercept
The y-intercept of the line shown is -6.

Video Examples: Graphing Linear Functions by Finding X,Y Intercept

Solved Examples on Y-Intercept

Ques: Find the y-intercept of the line shown in the graph.

Solved Examples on y-intercept

Choices:

A. - 3
B. 0
C. 3
D. 1
Correct Answer: A

Solution:

Step 1: The y-coordinate of the point where a line intersects the y-axis is the y-intercept of that line.
Step 2: The graph of the line crosses the y-axis at (0, - 3).
Step 3: So, the y-intercept of the line is - 3.

Quick Summary

The y-intercept is the point where the line crosses the y-axis.
At the y-intercept, the x-coordinate is always 0.
The y-intercept can be found by substituting x=0 into the equation of the line.

\[ y = mx + b, where b is the y-intercept \]

⚠️ Common Mistakes

Confusing the y-intercept with the x-intercept.
Incorrectly identifying the y-intercept from a graph.
Forgetting to set x=0 when calculating the y-intercept from an equation.

🌍 Real-World Uses

Initial value in linear depreciation: The y-intercept represents the initial cost of an asset before depreciation begins.
Starting fee for a service: A plumber charges a flat rate (y-intercept) plus an hourly fee (slope). The y-intercept is the initial service fee.
Water level in a tank before filling: If water is being added to a tank at a constant rate, the y-intercept represents the initial water level.

📋 Standards Alignment

CCSS.MATH.CONTENT.8.EE.C.7
CCSS.MATH.CONTENT.HSA.REI.C.6

🍎 Teacher Insights

Use visual aids like graphs to help students understand the concept. Emphasize the importance of x=0 at the y-intercept. Provide plenty of practice problems.

🎓 Prerequisites

Coordinate Plane
Linear Equations
Slope

Check Your Knowledge

Q1: What is the y-intercept of the line y = 2x + 3?

0 2 3 5

Q2: A line passes through the points (0, 5) and (2, 9). What is the y-intercept?

0 2 5 9

Frequently Asked Questions

Q: How do I find the y-intercept from a graph?
A: Look for the point where the line crosses the y-axis. The y-coordinate of that point is the y-intercept.

Q: How do I find the y-intercept from an equation?
A: Substitute x=0 into the equation and solve for y. The resulting y-value is the y-intercept.