Math Problem Statement

Which statement is true?

  1. The y intercept of function a is greater than the y intercept of function b.

  2. The y intercept of function b is greater than the y intercept of function a

Which statement is true? 1. The y intercept of function A is greater than the y intercept of function B. 2. The y intercept of function B is greater than the y intercept of function A.

Solution

To determine which statement is true, let's analyze the yy-intercepts of both functions:

  1. Function A (from the graph):

    • The green line in the graph intercepts the yy-axis at y=0y = 0.
  2. Function B (given as y=2x1y = 2x - 1):

    • The equation y=2x1y = 2x - 1 has a yy-intercept of 1-1, as seen from the constant term 1-1 when x=0x = 0.

Comparison of y-intercepts:

  • The yy-intercept of Function A is 00.
  • The yy-intercept of Function B is 1-1.

Since 0>10 > -1, the y-intercept of Function A is greater than the y-intercept of Function B.

Answer:

Statement 1 is true: The y-intercept of function A is greater than the y-intercept of function B.

Would you like further explanation on this? Here are some related questions:

  1. How do you find the y-intercept of a function from its equation?
  2. What does the slope of a function tell us about its graph?
  3. How can you determine if two lines are parallel based on their equations?
  4. What are some methods for finding the x-intercept of a linear function?
  5. How does the value of the y-intercept affect the graph of a linear function?

Tip: The y-intercept of a linear function y=mx+by = mx + b is always the constant bb in the equation.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Functions

Formulas

Slope-intercept form y = mx + b

Theorems

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Suitable Grade Level

Grades 7-9