You have the following equations:
[tex]\begin{gathered} y=5x \\ 5x+y=4 \end{gathered}[/tex]In order to determine if the given lines are parallel, pependicular or neither, first write the second equation in the slope y-intercept form, just as follow:
[tex]y=-5x+4[/tex]the coefficient of the term with variable x is the slope of the line. Thus, you have that the first line has a slope of m1=5 and the second line a slope of m2=-5
If the quotient between the slope of the lines is equal to -1, it means that the lines are perpendicular. You have:
[tex]\frac{m_1}{m_2}=-1[/tex]Hence, the lines are perpendicular
