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

Your Progress

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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