Answer: The required equation of the line is \(4x+y=6.\)
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:
\(4x+y-1=0~~~~~~~~~~~~~~~~~~~~~~~~~(i)\)
The slope-intercept form of the given line (i) is
\(4x+y-1=0\\\\\Rightarrow 4x+y=1\\\\\Rightarrow y=-4x+1,\)
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
\(y-2=m(x-1)\\\\\Rightarrow y-2=-4(x-1)\\\\\Rightarrow y-2=-4x+4\\\\\Rightarrow 4x+y=6.\)
Thus, the required equation of the line is \(4x+y=6.\)
