Use the guided visualization to answer the question. Click here to open the guided visualization. Leave Point B at $$ (-1,3) $$. Now move Point A towards $$ (-1,3) $$. What value does the slope of the secant line approach? The slope of the secant line approaches (Type a whole number.)

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To determine the slope of the secant line as Point A moves towards Point B at $$ (-1, 3) $$, we need to understand the concept of the slope of a secant line.

The slope $$ m $$ of a secant line between two points $$ A(x_1, y_1) $$ and $$ B(x_2, y_2) $$ is given by the formula:

$$
m = \frac{y_2 - y_1}{x_2 - x_1}
$$

In this case, Point B is fixed at $$ (-1, 3) $$. As Point A moves towards Point B, its coordinates can be represented as $$ A(x_1, y_1) $$, where $$ x_1 $$ approaches $$-1$$ and $$ y_1 $$ approaches $$3$$.

As Point A approaches Point B, both $$ x_1 $$ and $$ y_1 $$ will get closer to $$-1$$ and $$3$$ respectively. Therefore, the slope of the secant line can be expressed as:

$$
m = \frac{3 - y_1}{-1 - x_1}
$$

As $$ A $$ approaches $$ B $$ (i.e., $$ x_1 \to -1 $$ and $$ y_1 \to 3 $$), the numerator $$ 3 - y_1 $$ approaches $$ 0 $$ and the denominator $$ -1 - x_1 $$ also approaches $$ 0 $$.

This means that the slope $$ m $$ approaches the form $$ \frac{0}{0} $$, which indicates that we need to analyze the behavior of the slope more closely.

If we consider the limit as $$ A $$ approaches $$ B $$, we can conclude that the slope of the secant line approaches the slope of the tangent line at that point. If we assume that the function represented by the points is continuous and differentiable at that point, the slope of the tangent line at $$ (-1, 3) $$ will be the value we are looking for.

If we assume that the function is linear or has a defined slope at that point, we can conclude that the slope approaches $$ 0 $$ as the two points converge vertically.

Thus, the slope of the secant line approaches:

$$
\boxed{0}
$$
The slope of the secant line approaches 0.

Use the guided visualization to answer the question. Click here to open the guided visualization. Leave Point B at \( (-1,3) \). Now move Point A towards \( (-1,3) \). What value does the slope of the secant line approach? The slope of the secant line approaches (Type a whole number.)

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