Answer: The required equation of the line is [tex]4x+y=6.[/tex]
Step-by-step explanation: We are given to find the equation of the line that passes through (1, 2) and is parallel to the line whose equation is as follows:
[tex]4x+y-1=0~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
The slope-intercept form of the given line (i) is
[tex]4x+y-1=0\\\\\Rightarrow 4x+y=1\\\\\Rightarrow y=-4x+1,[/tex]
where, slope of the line is, m = - 4.
Since parallel lines have equal slopes, so the slope of the new line that passes through the point (1, 2) is
m = - 4.
Therefore, the equation of the line will be
[tex]y-2=m(x-1)\\\\\Rightarrow y-2=-4(x-1)\\\\\Rightarrow y-2=-4x+4\\\\\Rightarrow 4x+y=6.[/tex]
Thus, the required equation of the line is [tex]4x+y=6.[/tex]
