From Förberedande kurs i matematik 1

The line should go through the points (5,0) and (0,-8) which must therefore satisfy the equation of the line \displaystyle y=kx+m, i.e.

\displaystyle 0=k\cdot 5+m\qquad\text{and}\qquad -8 = k\cdot 0+m\,\textrm{.}

From the second equation, we get \displaystyle m=-8 and substituting this into the first equation gives

\displaystyle 0=5k-8\quad\Leftrightarrow\quad k={8}/{5}\,\textrm{.}

The slope of the line is 8/5.