This online calculator can find and plot the equation of a straight line passing through the two points. The calculator will generate a stepbystep explanation on how to obtain the result.

To find equation of the line passing through points $A(x_A, y_A)$ and $B(x_B, y_B)$ ( $ x_A \ne x_B $ ), we use formula:
$$ {\color{blue}{ y  y_A = \frac{y_B  y_A}{x_Bx_A}(xx_A) }} $$Example:
Find the equation of the line determined by $A(2, 4)$ and $B(3, 2)$.
Solution:
In this example we have: $ x_A = 2,~~ y_A = 4,~~ x_B = 3,~~ y_B = 2$. So we have:
$$ \begin{aligned} y  y_A & = \frac{y_B  y_A}{x_Bx_A}(xx_A) \\ y  4 & = \frac{2  4}{3  (2)}(x  (2)) \\ y  4 & = \frac{6}{5}(x + 2) \end{aligned} $$Multiply both sides with $5$ to get rid of the fractions.
$$ \begin{aligned} (y  4)\cdot {\color{red}{ 5 }} & = \frac{6}{5}\cdot {\color{red}{ 5 }}(x + 2)\\ 5y  20 & = 6(x + 2)\\ 5y  20 & = 6x  12 \\ 5y & = 6x  12 + 20 \\ 5y & = 6x + 8 \\ {\color{blue}{ y }} & {\color{blue}{ = \frac{6}{5}x  \frac{8}{5} }} \end{aligned} $$In special case (when $x_A = x_B$ the equation of the line is:
$$ {\color{blue}{ x = x_A }} $$Example 2:
Find the equation of the line determined by $A(2, 4)$ and $B(2, 1)$.
Solution:
In this example we have: $ x_A = 2,~~ y_A = 4,$ $ x_B = 2,~~ y_B = 1$. Since $x_A = x_B$, the equation of the line is:
$$ {\color{blue}{ x = 2 }} $$You can see from picture on the right that in special case the line is parallel to y  axis.
Note: use above calculator to check the results.
Please tell me how can I make this better.
48 904 215 solved problems