As a subject matter expert in mathematics, I can guide you through the process of finding the Y-intercept of a line given two points. The Y-intercept is the point where a line crosses the Y-axis, and it is represented as an ordered pair (0, y), where '0' is the X-coordinate and 'y' is the Y-coordinate.

To find the Y-intercept, you can use the following steps:


1. Identify the two points: Let's call them Point A and Point B.
2. **Write the equation of the line in slope-intercept form**: The general form is y = mx + b, where 'm' is the slope and 'b' is the Y-intercept.

3. Calculate the slope (m): The slope is calculated using the formula \( m = \frac{y_2 - y_1}{x_2 - x_1} \), where (x_1, y_1) and (x_2, y_2) are the coordinates of the two points.
4. **Plug one of the points and the slope into the equation**: This will give you an equation with 'b' as the unknown.

5. Solve for 'b': This will give you the Y-intercept.

Here's an example:

Suppose you have two points, Point A (3, 4) and Point B (6, 8). First, calculate the slope:

\[ m = \frac{8 - 4}{6 - 3} = \frac{4}{3} \]

Now, plug one of the points into the equation and solve for 'b':

\[ 4 = \frac{4}{3} \cdot 3 + b \]

Solving for 'b' gives us:

\[ b = 4 - 4 = 0 \]

So, the Y-intercept is at the point (0, 0).

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Identify the slope, m. This can be done by calculating the slope between two known points of the line using the slope formula.Find the y-intercept. This can be done by substituting the slope and the coordinates of a point (x, y) on the line in the slope-intercept formula and then solve for b.read more >>