3.6. A line is given by the equation with the slope $y=3 x-4$

1) write the equation of the line parallel to the given one and passing through the point $\left.P_{0}=(1 ; 2) ; 2\right)$ write the equation of the line perpendicular to the given one and passing through the point $P_{0}=(1 ; 2)$.
Solution.

1) Based on the condition of parallelism (3.14) of two lines given by equations with angular coefficients $k_{2}=k_{1}=3$, using formula (3.5), we obtain that the required equation has the form $y-2=3(x-1)$ or $y=3 x-1$;
2) Based on the condition (3.15) of perpendicularity of two lines, we get $k_{2}=-1 / k_{1}=-1 / 3$. Again using formula (3.5), we obtain

$$
y-2=-\frac{1}{3}(x-1) \text { or } y=-\frac{1}{3} x+\frac{7}{3} \text {. }
$$