Pre-AlgebraY-Intercept
Understanding Y-Intercept
Learn about y-intercepts, how to find them, and their importance in linear equations.
What is a Y-Intercept?
Definition
- The point where a line crosses the y-axis
- Always has an x-coordinate of 0
- Written as (0, b) where b is the y-value
- Important in understanding linear equations
Finding the Y-Intercept
- From a graph: Look where the line crosses the y-axis
- From an equation (y = mx + b): The value of b
- From a table: Find the y-value when x = 0
- From a word problem: Initial value often represents y-intercept
Slope-Intercept Form
The equation y = mx + b is in slope-intercept form where:
- m is the slope
- b is the y-intercept
- This form makes it easy to identify the y-intercept
- Any linear equation can be rewritten in this form
Real-World Applications
- Initial value in growth/decay problems
- Starting point in linear relationships
- Fixed costs in business problems
- Base price in pricing models
Practice Problems
Problem 1
Find the y-intercept in the equation: y = 2x + 5
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Related Topics
Quick Tips
- The y-intercept is where x = 0
- In y = mx + b, b is the y-intercept
- Look for initial values in word problems