Scatter Plot: Roses vs Lilies in Flower Bunches

Answer

The scatter plot displays data points where the horizontal axis ($x$-axis) represents the number of lilies and the vertical axis ($y$-axis) represents the number of roses. By reading the coordinates $(x, y)$ of each point, we can determine the exact composition of each flower bunch.

Explanation

I have analyzed the provided scatter plot. Each green "x" represents a specific bunch of flowers. The position of each "x" is determined by its horizontal distance from the left (representing the number of lilies) and its vertical distance from the bottom (representing the number of roses).

1. Identifying the data points To find the number of roses in a bunch with a specific number of lilies, we locate the number on the horizontal axis and move upward to find the marked "x". The coordinate pair is written as (number of lilies, number of roses). Looking at the graph, we can list the coordinates $(L, R)$ for all points: $(1, 2), (1, 7), (2, 9), (3, 6), (5, 5), (5, 9), (7, 1), (7, 6), (7, 8), (8, 3), (8, 7)$

2. Interpreting the coordinates Each coordinate $(L, R)$ means $L$ lilies are paired with $R$ roses in a single bunch. For example, the point at $(5, 5)$ indicates a bunch containing exactly $5$ lilies and $5$ roses. The relationship between the variables can be represented as: $P = (L, R)$ This formula represents a point on the grid where $L$ is the independent variable (lilies) and $R$ is the dependent variable (roses).

3. Analyzing specific values If you need to know how many roses are in a bunch with $7$ lilies, you look at the $x$-value of $7$. We see three points: $(7, 1), (7, 6),$ and $(7, 8)$. This tells us there are three different bunches that contain $7$ lilies, containing either $1, 6,$ or $8$ roses respectively.

Final Answer

The scatter plot illustrates the distribution of roses across different quantities of lilies. The data points represent $(Number \ of \ lilies, Number \ of \ roses)$. For any given number of lilies, the graph reveals the corresponding count of roses:
$\boxed{(1, 2), (1, 7), (2, 9), (3, 6), (5, 5), (5, 9), (7, 1), (7, 6), (7, 8), (8, 3), (8, 7)}$

Common Mistakes

• Swapping the axes: A very common error is reading the vertical axis value as the $x$-coordinate. Always remember "Run then Rise"—move along the horizontal axis first, then move up the vertical axis.
• Missing overlapping/multiple points: Students often assume each $x$-value (number of lilies) can only have one corresponding $y$-value (number of roses). As seen above, one quantity of lilies can be associated with several different quantities of roses (e.g., $7$ lilies appear with $1, 6,$ and $8$ roses).