How to Find the Y Intercept with two points

Last updated on February 2nd, 2022

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 $\dpi{150} \mathbf{Y-Y_{1} = m(X-X_{1})}$ .

Steps

Calculate the slope from 2 points.
$\dpi{150} Slope = \frac{Y_{2}-Y_{1}}{X_{2}-X_{1}} = \frac{Rise}{Run} = \frac{\bigtriangleup Y}{\bigtriangleup X}$

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

$Slope = \frac{Y_{2}-Y_{1}}{X_{2}-X_{1}} = \frac{11 - 5}{6 - 3} = \frac{6}{3} = 2$
Substitute the slope(m) in the slope-intercept form of the equation.
$\\y = mx+b \\y = 2x+b$
Substitute either point into the equation. You can use either (3,5) or(6,11).

$\\y = 2x+b \\5 = 2(3)+b$
Solve for b, which is the y-intercept of the line.
$\\5 \ \ \ = 2(3) + b \\5 \ \ \ = 6 + b \\\underline{-6\ = -6 \ \ \ \ \ \ \ } \\-1 = b$
Substitute b, into the equation.
$\\y = 2x + b \\y = 2x - 1$

Equation from 2 points using Slope-Intercept Form

Steps

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