Let's break this down into two parts, as required by the question:

1. Plotting the Ordered Pairs:

The table gives the following ordered pairs $(x, y)$, where $x$ represents the number of filled seats and $y$ represents the number of open seats:

• (3, 15)
• (7, 11)
• (8, 10)
• (13, 5)

These pairs can be plotted on a coordinate plane, with $x$ on the horizontal axis and $y$ on the vertical axis.

2. Writing an Equation Relating $x$ and $y$:

To find the equation, we assume the relationship between $x$ (filled seats) and $y$ (open seats) is linear. The general form of a linear equation is: $y = mx + b$ Where:

• $m$ is the slope
• $b$ is the y-intercept

Let's calculate the slope $m$ using the two points $(3, 15)$ and $(13, 5)$: $m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{5 - 15}{13 - 3} = \frac{-10}{10} = -1$

So, the slope is $m = -1$.

Now, we can use one of the points to solve for the y-intercept $b$. Using the point $(3, 15)$: $15 = -1(3) + b \implies 15 = -3 + b \implies b = 18$

Thus, the equation relating $x$ and $y$ is: $y = -x + 18$

Summary:

• Ordered pairs: (3, 15), (7, 11), (8, 10), (13, 5)
• Equation: $y = -x + 18$

Would you like further details or help with graphing?

Here are 5 related questions:

1. How do you calculate the slope between two points?
2. What is the significance of the y-intercept in the equation?
3. How can you use substitution to verify the equation?
4. What would happen if the data were not linear?
5. How can you determine if a system is over- or under-constrained?

Tip: Always check if a relationship appears linear before assuming a linear equation!