$(d): (m-1)x + (3m-4)y = -2m-5 \Leftrightarrow y= \dfrac{1-m}{3m-4}x + \dfrac{-2m-5}{3m-4}$
a) $(d)$ song song với trục hoành $\Leftrightarrow
\left\{\begin{matrix}
\dfrac{1-m}{3m-4} \neq 0 \\ \dfrac{-2m-5}{3m-4} \neq 1 \\ 3m-4 \neq 0
\end{matrix}\right. \\
\Leftrightarrow
\left\{\begin{matrix}
1-m \neq 0 \\ \dfrac{-2m-5}{3m-4} -1 \neq 0 \\ m \neq \dfrac{4}{3}
\end{matrix}\right. \\
\Leftrightarrow
\left\{\begin{matrix}
m \neq 1 \\ \dfrac{-5m+1}{3m-4} \neq 0 \\ m \neq \dfrac{4}{3}
\end{matrix}\right. \\
\Leftrightarrow
\left\{\begin{matrix}
m \neq 1 \\ m \neq \dfrac{1}{5} \\ m \neq \dfrac{4}{3}
\end{matrix}\right. \\
$
Vậy $m \neq \left \{ \dfrac{1}{5}; 1; \dfrac{4}{3} \right \}$
b) $(d)$ song song với trục tung $\Leftrightarrow
\left\{\begin{matrix}
\dfrac{1-m}{3m-4} \neq 1 \\ \dfrac{-2m-5}{3m-4} \neq 0 \\ 3m-4 \neq 0
\end{matrix}\right. \\
\Leftrightarrow
\left\{\begin{matrix}
\dfrac{1-m}{3m-4}-1 \neq 0 \\ -2m-5 \neq 0 \\ m \neq \dfrac{4}{3}
\end{matrix}\right. \\
\Leftrightarrow
\left\{\begin{matrix}
\dfrac{-4m+5}{3m-4} \neq 0 \\ m \neq \dfrac{-5}{2} \\ m \neq \dfrac{4}{3}
\end{matrix}\right. \\
\Leftrightarrow
\left\{\begin{matrix}
m \neq \dfrac{5}{4} \\ m \neq \dfrac{-5}{2} \\ m \neq \dfrac{4}{3}
\end{matrix}\right. \\
$
Vậy $m \neq \left \{ \dfrac{-5}{2};\dfrac{5}{4} ; \dfrac{4}{3} \right \}$
c) $(d)$ đi qua gốc toạ độ $\Leftrightarrow
\left\{\begin{matrix}
\dfrac{1-m}{3m-4} \neq 0 \\ \dfrac{-2m-5}{3m-4}=0 \\ 3m-4 \neq 0
\end{matrix}\right. \\
\Leftrightarrow
\left\{\begin{matrix}
m \neq 1 \\ -2m-5=0 \\ m \neq \dfrac{4}{3}
\end{matrix}\right. \\
\Leftrightarrow
\left\{\begin{matrix}
m \neq 1 \\ m = \dfrac{-5}{2} \\ m \neq \dfrac{4}{3}
\end{matrix}\right. \\
\Leftrightarrow m = - \dfrac{5}{2}$
d) $(d)$ đi qua $A(2;1)$ $\Leftrightarrow (m-1).2+ (3m-4).1 = -2m-5 \\
\Leftrightarrow 7m-1=0 \Leftrightarrow m = \dfrac{1}{7}$
[TẶNG BẠN] TRỌN BỘ Bí kíp học tốt 08 môn
