Question

How do you find the Y intercept with $2$ points?

Answer 1

Find the y-intercept with $2$ points:

Let $(x_1,y_1)$ and $(x_2,y_2)$ be the two given points.

Slope of the line passing through the given points is:

$m=\frac{y_2-y_1}{x_2-x_1}$

The equation of a line in slope-intercept form is:

$y=mx+c$

Here, $m$ is the slope of the line and $c$ is the y-intercept.

Now, substitute the two points in $m=\frac{y_2-y_1}{x_2-x_1}$ to find the value of $m$ and substitute the value of $m$ and one of the point in $y=mx+c$. The value of $c$ is the y-intercept.

For example, Let $(1,2)$ and $(-2,-3)$ be two points of line. Then slope of the line is

$m=\frac{y_2-y_1}{x_2-x_1}=\frac{-3-2}{-2-1}=\frac{5}{3}$

Substitute $y=2,x=1,m=\frac{5}{3}$ in $y=mx+c$

$$\begin{gathered} 2=\frac{5}{3}\times 1+c \\ c=\frac{1}{3} \end{gathered}$$

Hence, the y-intercept of the line is $\frac{\mathbf{1}}{\mathbf{3}}$.