Explicit equation of the straight line

From the general equation of the straight line:

$A x + B y + C = 0$

We can isolate $y$ and we obtain:

$y = - \frac{A}{B} x - \frac{C}{B}$

which is equivalent to:

$y = m \cdot x + n$

where $m = - \frac{A}{B}$ is the slope of the straight line, and $n = - C / B$ is $y$ -coordinate of the point of intersection of the straight line with the axis $O Y$ ; in other words, the value of $y$ when $x = 0$ , that is to say $y (0) = f (0)$ .

Example

Find the explicit equation of the straight line $r$ with implicit equation:

$2 x + 5 y - 26 = 0$

Therefore, isolating $y$ :

$y = - \frac{2}{5} x + \frac{26}{5}$

where we see that the straight line has slope $- \frac{2}{5}$ and that it cuts the axis $O Y$ in $y = \frac{26}{5}$ , or at point $(0, \frac{26}{5})$ .