1. Using Graphs to Relate Two Quantities
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How is the area of a rectangle related to its width?
See solution.
There are infinitely many real-world relationships between the area of a rectangle and its width. We will only illustrate one of them.
Imagine that a farmer wants to mow some of the grass in his garden. He wants the area to be a rectangle with a specific length. He wonders how much more lawn he would need to mow if he increased the width of this piece of land.
We will now sketch a graph modeling the situation using numerical values. Let's recall the formula for the area of a rectangle. A =l * w Here, l is the length and w is the width. We can use any arbitrary value for the length and then find some values for the area by changing the value of w. For example, if we use l = 100, then we can find the area when w=2 by using the above formula.
Considering l =100 and changing the value of w, we can do the same calculation multiple times. With this process, we will generate enough points to sketch our graph.
| w | l * w | A |
|---|---|---|
| 0 | 100* 0 | 0 |
| 2 | 100* 2 | 200 |
| 4 | 100* 4 | 400 |
| 6 | 100* 6 | 600 |
| 8 | 100* 8 | 800 |
Now we can sketch our graph by plotting the points and joining them with a straight line.
