From Förberedande kurs i matematik 1

Because the straight line is to have a slope of \displaystyle -3, its equation can be written as

\displaystyle y=-3x+m\,,

where m is a constant. If the line is also to pass through the point (x,y) = (1,-2), the point must satisfy the equation of the line,

\displaystyle -2=-3\cdot 1+m\,,

which gives that \displaystyle m=1.

The answer is thus that the equation of the line is \displaystyle y=-3x+1.