Math Problem Statement

Which answer choice best describes f(x) = x - 12?

Solution

The problem on your screen is asking for the best description of the function f(x)=x12f(x) = x - 12.

Step-by-step analysis:

  1. Function Form: f(x)=x12f(x) = x - 12 is a linear function because it can be written in the slope-intercept form y=mx+by = mx + b, where mm is the slope, and bb is the y-intercept. Here:

    • The slope m=1m = 1 (since the coefficient of xx is 1),
    • The y-intercept b=12b = -12.
  2. Linear Variation: A direct linear variation implies that there is a constant rate of change, and this rate is represented by the slope mm. In this case, the constant variation is 1, as that is the slope of the function.

  3. Answer: The best answer is:
    "The relationship shows a direct linear variation with a constant of variation of 1."

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Relative Questions:

  1. What is the general form of a linear function?
  2. How can we find the slope of a linear function?
  3. How does the y-intercept affect the graph of a linear function?
  4. What is the meaning of "direct variation" in linear functions?
  5. Can a

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Math Problem Analysis

Mathematical Concepts

Linear Functions
Slope-Intercept Form

Formulas

y = mx + b

Theorems

Direct Linear Variation
Slope of a Line

Suitable Grade Level

Grades 6-8