From Förberedande kurs i matematik 1

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

\displaystyle y=-3x+m

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

\displaystyle -2=-3\centerdot 1+m

which gives that \displaystyle m=1.

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