Solution:
We are required to determine if the two lines are parallel
Note that if two lines are parallel, they must have equal slope.
[tex]\begin{gathered} For\text{ line y=}\frac{x}{4}+5 \\ y=\frac{1}{4}x+5 \\ The\text{ slope of this line = 1/4} \end{gathered}[/tex]
For the second line, calculate the slope
[tex]\begin{gathered} Slope\text{ = }\frac{change\text{ in y}}{change\text{ in x}} \\ \\ Slope=\frac{2-1}{4-0} \\ Slope\text{ = }\frac{1}{4} \\ \end{gathered}[/tex]
Since the two lines have equal slopes (1/4) then they are parallel
