Math Problem Statement

One of the graphs could show that T is inversely proportional to x. Write down the letter of this graph.

Solution

The question asks which graph shows that TT is inversely proportional to xx.

When two variables are inversely proportional, their relationship can be described as:

T1xT \propto \frac{1}{x}

This means as xx increases, TT decreases, and vice versa, and the graph of TT versus xx will have a downward curve that approaches the axes but never touches them.

Looking at the graphs:

  • Graph D shows a curve that decreases as xx increases, which is the characteristic shape of an inverse proportionality.

Thus, the correct graph is D.

Do you have any questions or want further details?

Here are five related questions to expand on this topic:

  1. What does it mean for two variables to be directly proportional?
  2. How would the graph of TxT \propto x look like?
  3. What are some real-life examples of inverse proportionality?
  4. How can we represent inverse proportionality algebraically?
  5. How do the slopes of these graphs change as xx increases?

Tip: Inverse proportional relationships often appear in situations involving rates, such as speed versus time, where increasing one decreases the other.

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Math Problem Analysis

Mathematical Concepts

Inverse Proportionality
Graphical Interpretation

Formulas

T ∝ 1/x

Theorems

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Suitable Grade Level

Grades 8-10