How do you find the Y intercept of two points?

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).

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.