# Given the coordinates of 2 points on a line, how do you find the y-intercept?

Mar 15, 2017

Use the two given points to generate a slope-point equation,
then substitute $0$ for $x$ to find the value of the y-intercept

#### Explanation:

If the two points are $\left({a}_{1} , {b}_{1}\right)$ and $\left({a}_{2} , {b}_{2}\right)$
then the slope-point equation is
$\textcolor{w h i t e}{\text{XXX}} y = \frac{{b}_{2} - {b}_{1}}{{a}_{2} - {a}_{1}} \cdot \left(x - {a}_{1}\right) + {b}_{1}$

So the y-intercept would be
$\textcolor{w h i t e}{\text{XXX}} y = {b}_{1} - {a}_{1} \left(\frac{{b}_{2} - {b}_{1}}{{a}_{2} - {a}_{1}}\right)$