Explicit equation of the straight line

From the general equation of the straight line:

$$Ax + By + C = 0$$

We can isolate $y$ and we obtain:

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

which is equivalent to:

$$y=m \cdot x+n$$

where $\displaystyle m =-\frac{A}{B}$ 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 $OY$; in other words, the value of $y$ when $x = 0$, that is to say $y (0) = f (0)$.

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

$$2x + 5y - 26 = 0$$

Therefore, isolating $y$:

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

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