Answer:
Given equation are:
[tex]y = -\frac{1}{4}x+8[/tex] ......[1]
[tex]-2x+8y = 4[/tex] .....[2]
- The two lines are parallel lines then their slopes will be equal.
- When two lines are perpendicular then, the slope of lines are the negative reciprocals of each other.
Now, Equation of a line is in the form of y =mx+b where m is the slope of the line.
Slope[tex](m_1)[/tex] of equation of line in [1] is;
[tex]y = -\frac{1}{4}x+8[/tex]
then;
[tex]m_1= -\frac{1}{4}[/tex]
Slope[tex](m_2)[/tex] of equation of line in [2];
[tex]-2x+8y = 4[/tex]
Add both sides 2x we get;
-2x + 8y + 2x = 2x + 4
Simplify:
8y = 2x +4
Divide both sides by 8 we get;
[tex]y = \frac{1}{4} x + \frac{1}{2}[/tex]
then;
[tex]m_2 = \frac{1}{4}[/tex]
Therefore, the given two lines are neither parallel nor perpendicular.
