To graph the line and determine its equation, let's follow these steps:

1. Find the slope of the line:

Given two points $(8, -3)$ and $(2, -3)$, we can calculate the slope using the slope formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Substitute the coordinates: $m = \frac{-3 - (-3)}{2 - 8} = \frac{0}{-6} = 0$

Since the slope $m = 0$, this indicates the line is horizontal.

2. Write the equation of the line:

For a horizontal line, the equation is always of the form: $y = c$ where $c$ is the constant value of $y$ for all points on the line.

In this case, since $y = -3$ for both points, the equation of the line is: $y = -3$

3. Graph the line:

The graph is a horizontal line passing through $y = -3$ on the $y$-axis. Every point on this line will have $y = -3$, regardless of the $x$-value.

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Questions:

1. What is the general form of the equation for a horizontal line?
2. Can a horizontal line ever have a non-zero slope?
3. How does a vertical line's equation differ from a horizontal line's?
4. What does a slope of zero represent in terms of real-life applications?
5. How would the equation change if the points were on a vertical line?

Tip: When the slope of a line is zero, it indicates that the line is horizontal and the $y$-coordinate remains constant for all $x$-values.