$$\eqalign{
& 1) \cr
& a)\,\,y = \left( {2m + 3} \right)x - m + 1 \cr
& Ham\,\,so\,\,dong\,\,bien\,\,tren\,\,R \Leftrightarrow 2m + 3 > 0 \Leftrightarrow m > - {3 \over 2} \cr
& b)\,\,y = m\left( {x + 2} \right) + x\left( {2m + 1} \right) \cr
& \,\,\,\,\,y = \left( {3m + 1} \right)x + 2m \cr
& Ham\,\,so\,\,NB\,\,tren\,\,R \Leftrightarrow 3m + 1 < 0 \Leftrightarrow m < - {1 \over 3} \cr
& 2) \cr
& a)\,\,He\,\,so\,\,goc\,\,bang\,\, - 2 \Rightarrow a = - 2 \cr
& Di\,\,qua\,\,A\left( {2;1} \right) \cr
& \Rightarrow 1 = \left( { - 2} \right).2 + b \Leftrightarrow b = 5 \cr
& \Rightarrow y = - 2x + 5 \cr
& b)\,\,Di\,\,qua\,\,M\left( {1;4} \right) \Rightarrow 4 = a + b \cr
& //\,\,y = 2x + 1 \Rightarrow a = 2,\,\,b \ne 1 \cr
& \Rightarrow 4 = 2 + b \Leftrightarrow b = 2 \cr
& \Rightarrow y = 2x + 2 \cr
& c)\,\,Di\,\,qua\,\,N\left( {4; - 1} \right) \Rightarrow - 1 = 4a + b \cr
& \bot \,\,4x - y + 1 = 0 \Leftrightarrow y = 4x + 1 \cr
& \Rightarrow a.4 = - 1 \Leftrightarrow a = - {1 \over 4} \cr
& \Rightarrow - 1 = 4.\left( { - {1 \over 4}} \right) + b \Leftrightarrow b = 0 \cr
& Vay\,\,y = - {1 \over 4}x \cr} $$
