What are the appropriate labels and…

Mathematics Questions

What are the appropriate labels and scales for the axes of the graph representing the relationship between the number of paving stones and the area of the patio?

Short Answer

To create a clear graph representing the relationship between stone length and patio area, define the x-axis for stone lengths in feet and the y-axis for patio area in square feet. Set appropriate scales, with the x-axis starting at 0 and counting by 1, and the y-axis starting at 0 and counting by 20, ensuring all values are represented and clearly labeled.

Step-by-Step Solution

Step 1: Define the Axes

To accurately represent the relationship between the length of stones and the patio area, we must define our axes. The x-axis will represent the length of each stone measured in feet, while the y-axis will represent the area of the patio measured in square feet. Clearly labeling these axes is crucial for understanding the graph.

Step 2: Set Appropriate Scales

Choosing the right scales for each axis is essential. For the x-axis, the data points of 3, 5, 6, and 7 suggest a scale starting at 0 and counting by 1 will capture all necessary values. In contrast, for the y-axis, the larger values of 36, 100, 144, and 196 require a scale starting at 0 and counting by 20 to ensure clarity and readability.

Step 3: Finalize Labels and Scales

With our axes and scales defined, we can finalize our graph. The x-axis should be labeled as “length of each stone (in feet)” with a scale starting at 0 and counting by 1. Simultaneously, the y-axis should be labeled as “area of the patio (in square feet)” with a scale starting at 0 and counting by 20. This will create a well-structured and informative graph.

Related Concepts

X-axis

The horizontal line on a graph representing one variable, in this case, the length of each stone measured in feet

Y-axis

The vertical line on a graph representing another variable, specifically the area of the patio measured in square feet

Scale

The set intervals by which the values on each axis increase, ensuring that all relevant data can be accurately displayed and understood.

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