[tex]d_1||d_2\Leftrightarrow m_{d_1}=m_{d_2}\\d_1:x+my=1\Rightarrow my=-x+1\Rightarrow y=\displaystyle-\frac{1}{m}x+\frac1m\Rightarrow m_{d_1}=-\frac1m\\\\d_2:mx+4y=5\Rightarrow 4y=-mx+5\Rightarrow y=-\frac{m}4x+\frac54\Rightarrow m_{d_2}=-\frac{m}{4}\\\\m_{d_1}=m_{d_2}\Leftrightarrow\displaystyle -\frac1m=-\frac{m}4\Rightarrow m^2=4\Rightarrow m_{1, 2}=\pm2[/tex]
