From Förberedande kurs i matematik 1
Two straight lines are parallel if they have the same gradient. From the line
y=3x+1, we can read off that it has a gradient of
3
(the coefficient in front of
x
), and hence the equation we are looking for has an equation of the form
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
2=3−1+m
which gives
m=5. Hence, the equation of the line is
y=3x+5.
