How to find y intercept with 2 points

When working on a math problem involving linear equations, you may find yourself with two specific points on a graph and need to determine where the line intersects the y-axis. This situation could arise in various contexts, from analyzing data trends to solving real-world problems that can be modeled with linear equations. Perhaps you’ve been given coordinates such as (3, 4) and (5, 6) and need to find the y-intercept to understand the relationship between the two points more clearly. In this case, you’re not just looking for a numerical value; you want to grasp the concept of how these points relate to the overall equation of the line they form.

The y-intercept can be found by using the formula for the slope-intercept form of a linear equation, which is y = mx + b. You can first calculate the slope (m) using the two points and then plug one of the points into the equation to solve for (b), the y-intercept.

To find the y-intercept using two points, you can follow these steps:

1. Identify the Points: Let’s say your two points are (x1, y1) and (x2, y2). For instance, point A could be (3, 4) and point B (5, 6).

2. Calculate the Slope (m): Use the slope formula:

\[

m = \frac{y2 – y1}{x2 – x1}

\]

Substituting the values from our example:

\[

m = \frac{6 – 4}{5 – 3} = \frac{2}{2} = 1

\]

3. Use the Point-Slope Form: After finding the slope, you can use one of the points and the slope to form the equation of the line. Using point A (3, 4):

\[

y – y1 = m (x – x1)

\]

becomes:

\[

y – 4 = 1(x – 3)

\]

4. Rearranging to Y-Intercept Form: Simplify this equation:

\[

y – 4 = x – 3

\]

which simplifies to:

\[

y = x + 1

\]

Here, the y-intercept (b) is 1.

In this example, through the calculations, we identified that the line intersects the y-axis at (0, 1), which is the y-intercept you were looking for.