# If you're given coordinates of 2 points, how do you find the y-intercept?

Jul 22, 2015

The y-intercept is $1$

#### Explanation:

Step 1.
Find the slope using the equation $m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$, where $m$ is the slope, and $\left({x}_{1} , {y}_{1}\right)$ and $\left({x}_{2} , {y}_{2}\right)$ are the two points on the line.

Example
Find the slope of a line passing through the points $\left(\textcolor{red}{- 2} , \textcolor{b l u e}{- 1}\right)$ and $\left(\textcolor{red}{4} , \textcolor{b l u e}{3}\right)$.

$\left(\textcolor{red}{- 2} , \textcolor{b l u e}{- 1}\right) = \left(\textcolor{red}{{x}_{1}} , \textcolor{b l u e}{{y}_{1}}\right)$

$\left(\textcolor{red}{4} , \textcolor{b l u e}{3}\right) = \left(\textcolor{red}{{x}_{2}} , \textcolor{b l u e}{{y}_{2}}\right)$

color(purple)m=(color(blue)(y_2)-color(blue)(y_1))/(color(red)(x_2)-color(red)(x_1))=(color(blue)(3)-(color(blue)(-1)))/(color(red)(4)-(color(red)(-2))=$\frac{\textcolor{b l u e}{4}}{\textcolor{red}{6}} = \frac{\textcolor{p u r p \le}{2}}{\textcolor{p u r p \le}{3}}$

Step 2.

Determine the point-slope form of a linear equation $\left(y - {y}_{1}\right) = m \left(x - {x}_{1}\right)$, where $\left({x}_{1} , {y}_{1}\right)$ is one of the points.

Continue with the previous example.

$\left(\textcolor{b l u e}{y} - \left(\textcolor{b l u e}{- 1}\right)\right) = \textcolor{p u r p \le}{\frac{2}{3}} \left(\textcolor{red}{x} - \left(\textcolor{red}{- 2}\right)\right)$ =

$\textcolor{b l u e}{y} + \textcolor{b l u e}{1} = \textcolor{p u r p \le}{\frac{2}{3}} \left(\textcolor{red}{x} + \textcolor{red}{2}\right)$

Convert to slope-intercept form $y = m x + b$, where $m$ is the slope and $b$ is the y-intercept, by solving for $y$.

$y + 1 = \frac{2}{3} x + 2$

Subtract $1$ from both sides.

$y = \frac{2}{3} x + 2 - 1$ =

$y = \frac{2}{3} x + 1$

The slope intercept is $1$.