describe a real world relationship between the area of a rectangle and its width, as the width varies and the length stays the same. Sketch a graph to show this relationship.
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The relationship between the area of a rectangle and its width can be described as follows: As the width of a rectangle varies while the length remains constant, the area of the rectangle will change. Specifically, as the width increases, the area of the rectangle increases, and as the width decreases, the area decreases.
To illustrate this relationship, we can sketch a graph. In the graph, the x-axis represents the width of the rectangle, and the y-axis represents the area of the rectangle. Since we are keeping the length constant, we can assume a fixed value for the length.
Let's assume the length of the rectangle is 5 units. We can create a table of values to demonstrate the relationship and plot points on the graph:
Width (x) Area (y)
--------------------------------
1 5
2 10
3 15
4 20
5 25
6 30
7 35
By plotting these points on the graph and connecting them with a line, we will obtain a linear relationship where the area increases proportionally with the width. Therefore, the graph will show a straight line that starts from the origin (0,0) and moves upward (positive slope).
Note that the scale and units on the axes will depend on the specific context of the problem.
A real-world example of the relationship between the area of a rectangle and its width can be seen in the construction of a rectangular garden bed. Let's consider a garden bed with a fixed length of 10 feet. As the width of the garden bed varies, the area it covers will change.
When the width is at its minimum, let's say 2 feet, the area of the garden bed will be 10 feet (length) multiplied by 2 feet (width), resulting in an area of 20 square feet.
As the width of the garden bed increases, the area will also increase. For example, if the width is 5 feet, the area will be 10 feet (length) multiplied by 5 feet (width), resulting in an area of 50 square feet.
Similarly, when the width increases to 8 feet, the area will be 10 feet (length) multiplied by 8 feet (width), giving an area of 80 square feet.
To sketch a graph representing the relationship between the area of the rectangle and its width, you can plot the widths on the x-axis and the corresponding areas on the y-axis.
The x-axis (width) can have values ranging from a minimum value to a maximum value. Let's say we choose a minimum width of 0 feet and a maximum width of 10 feet.
The y-axis (area) can have values ranging from the minimum area to the maximum area. In this case, we can select a minimum area of 0 square feet and a maximum area of 100 square feet.
Plotting the points for different widths and their corresponding areas, you will notice that as the width increases, the area also increases. This will result in a straight line that slopes upward from the origin (0, 0) to the point (10, 100).