The given eqation is:
[tex]y=4x+1[/tex]
Notice that the slope of the line is 4
Recall that the slopes of parallel lines are equal
Hence the slope of the required line is 4.
Since the line passes through the point (5,1)
The equation is:
[tex]y-1=4(x-5)[/tex]
This is simplified to give:
[tex]\begin{gathered} y-1=4x-20 \\ y-4x=-20+1 \\ -4x+y=-19 \\ 4x-y=19 \end{gathered}[/tex]
Therefore the equation of the line is:
[tex]4x-y=19[/tex]
