From Förberedande kurs i matematik 1

Two straight lines are parallel if they have the same gradient. From the line \displaystyle y=3x+1, we can read off that it has a gradient of \displaystyle 3 (the coefficient in front of \displaystyle x ), and hence the equation we are looking for has an equation of the form

\displaystyle y=3x+m

where \displaystyle m is a constant. The condition that the line should also contain the point \displaystyle \left( -1 \right.,\left. 2 \right) means that the point should satisfy the equation of the line

\displaystyle 2=3\left( -1 \right)+m

which gives \displaystyle m=5. Hence, the equation of the line is \displaystyle y=3x+5.