Given:
The equation of line is,
[tex]\begin{gathered} y=5x-2\Rightarrow5x-y-2=0\ldots\ldots\ldots\ldots........(1) \\ x+4y=8\Rightarrow x+4y-8=0\ldots.\ldots..\ldots...(2) \end{gathered}[/tex]For the equation,
[tex]\begin{gathered} A_1x+B_1y+C_1=0 \\ A_2x+B_2y+C_2=0 \end{gathered}[/tex][tex]\begin{gathered} \text{Parallel line if : }\frac{A_1}{A_2}=\frac{B_1}{B_2} \\ \text{ Coinside line if : }\frac{A_1}{A_2}=\frac{B_1}{B_2}=\frac{C_1}{C_2} \\ \text{Intersect line if : }\frac{A_1}{A_2}\ne\frac{B_1}{B_2} \end{gathered}[/tex]For the given equation of lines,
[tex]\begin{gathered} \frac{A_1}{A_2}=\frac{5}{1} \\ \frac{B_1}{B_2}=-\frac{1}{4} \\ \Rightarrow\frac{A_1}{A_2}\ne\frac{B_1}{B_2} \end{gathered}[/tex]Hence, the given lines are intersect each other.
