# How to Find the Y Intercept with two points

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Last updated on September 25th, 2020

The y-intercept of an equation is a point where the graph of the equation intersects the Y-axis. There are a few different ways to find the y-intercept with 2 points. Here is how you can find the Y-intercept with the equation from 2 points using the slope-intercept form.

## Equation from 2 points using Slope-Intercept Form

The Y-intercept with 2 points can be solved using the slope-intercept form in the equation. The point-slope form is $\dpi{150}&space;\mathbf{Y-Y_{1}&space;=&space;m(X-X_{1})}$.

## Steps

1. Calculate the slope from 2 points.

$\dpi{150}&space;Slope&space;=&space;\frac{Y_{2}-Y_{1}}{X_{2}-X_{1}}&space;=&space;\frac{Rise}{Run}&space;=&space;\frac{\bigtriangleup&space;Y}{\bigtriangleup&space;X}$

For Example, Two points are (3, 5) and (6, 11)

$Slope&space;=&space;\frac{Y_{2}-Y_{1}}{X_{2}-X_{1}}&space;=&space;\frac{11&space;-&space;5}{6&space;-&space;3}&space;=&space;\frac{6}{3}&space;=&space;2$

2. Substitute the slope(m) in the slope-intercept form of the equation.

$\\y&space;=&space;mx+b&space;\\y&space;=&space;2x+b$

3. Substitute either point into the equation. You can use either (3,5) or(6,11).

$\\y&space;=&space;2x+b&space;\\5&space;=&space;2(3)+b$

4. Solve for b, which is the y-intercept of the line.

$\\5&space;\&space;\&space;\&space;=&space;2(3)&space;+&space;b&space;\\5&space;\&space;\&space;\&space;=&space;6&space;+&space;b&space;\\\underline{-6\&space;=&space;-6&space;\&space;\&space;\&space;\&space;\&space;\&space;\&space;}&space;\\-1&space;=&space;b$

5. Substitute b,  into the equation.

$\\y&space;=&space;2x&space;+&space;b&space;\\y&space;=&space;2x&space;-&space;1$