Math Problem Statement

Write the ordered pair (x, y) that represents the unit rate of this graph.

Solution

In the graph provided, the horizontal axis represents the square meters of fabric, and the vertical axis represents the total cost in dollars.

To find the unit rate, we can look for a point on the graph where the coordinates are clear and then calculate the rate of change (the slope), which is the "rise over run." From the graph, two clear points appear to be (0, 0) and (3, 18).

The unit rate can be calculated as:

Unit rate=Change in yChange in x=18030=183=6\text{Unit rate} = \frac{\text{Change in y}}{\text{Change in x}} = \frac{18 - 0}{3 - 0} = \frac{18}{3} = 6

This means the cost per square meter of fabric is $6.

The ordered pair that represents the unit rate (for 1 square meter of fabric) would be:

(1,6)(1, 6)

Would you like further details or have any questions?

Here are 5 related questions to explore:

  1. What does the unit rate represent in a real-world scenario?
  2. How would the graph look if the unit rate was $8 per square meter?
  3. How can we calculate the total cost for 7 square meters using the unit rate?
  4. How do you find the slope from a graph in general?
  5. What happens if the cost of fabric per square meter increases over time?

Tip: The unit rate is often represented by the slope in linear graphs and shows how one quantity changes in relation to another.

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Math Problem Analysis

Mathematical Concepts

Unit Rate
Slope
Linear Relationships
Graph Interpretation

Formulas

Unit Rate = (Change in y) / (Change in x)

Theorems

Slope of a Line in Linear Graphs

Suitable Grade Level

Grades 6-8