From Förberedande kurs i matematik 1

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

\displaystyle y=3x+m\,,

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

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

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