Calculate $y$-intercept of line How can I use the coordinates of two points on a line and/or the slope to calculate the $y$-intercept? I really need to know.
 A: The equation of a line is given by $y=mx+b$, where $m$ is the slope of the line and $b$ is the y-intercept.
If you are given two points $(x_1,y_1)$ and $(x_2,y_2)$, then you can find the slope of the line passing through these points: $m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}$.
Then you can substitute the value of $x$ and $y$ using one of the points that you know your line passes through. So now you know the values of $x,y$ and $m$. Now you have enough information to isolate for $b$.
Example
Suppose a line passes through two points $A(1,2)$ and $B(4,6)$.
Then we first find the slope of this line. 
$m=\frac{\Delta y}{\Delta x}=\frac{6-2}{4-1}=\frac{4}{3}$
Now we use one of our points to get values for $x$ and $y$. I decide for no reason to use point $B$, so $x=4$ and $y=6$. Plugging this information into the equation of a line gives me that:
$y=mx+b\implies6=\frac{4}{3}\cdot 4+b\implies b=6-\frac{16}{3}=\frac{2}{3}$.
Hence the equation of the line is $y=\frac{4}{3}x+\frac{2}{3}$, and more relevantly to your question, the y-intercept of this line is $\frac{2}{3}$.
A: i am going to assume you have two points $(x_1,y_1)$ and $(x_2,y_2).$ the slope is the ratio of rise to run so it is $$\text{ slope } = \dfrac{y_2-y_1}{x_2-x_1}. \tag 1 $$
the $y$-intercept is the point on the $y$ axis therefor has coordinates $(0, c),$ where $c$ is called the $y-$ intercept. you set $y_2 = 0, x = 0$ in the slope formula to get $$\text{ slope}= \dfrac{c-y_1}{0-x_1} $$
from $(2),$ you can get $$c = y_1 - x_1 \times \text{ slope} $$
i will work the same example kunalan did. $(x_1,y_1) = (1,2), (x_2, y_2) = (4,6).$
then $\text{slope} = \dfrac{6-2}{4-1}=\dfrac43, c = 2- 1 \times \frac43 =\frac23.  $
