Question

16. Tell whether the lines for each pair of equations are parallel, perpendicular, or neither.

Answer 1

Answer:

Given equation are:

$y = -\frac{1}{4}x+8$                  ......[1]

$-2x+8y = 4$                             .....[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$(m_1)$ of equation of line in [1] is;

$y = -\frac{1}{4}x+8$  

then;

$m_1= -\frac{1}{4}$

Slope$(m_2)$ of equation of line in [2];

$-2x+8y = 4$

Add both sides 2x we get;

-2x + 8y + 2x = 2x + 4

Simplify:

8y = 2x +4

Divide both sides by 8 we get;

$y = \frac{1}{4} x + \frac{1}{2}$

then;

$m_2 = \frac{1}{4}$

Therefore, the given two lines are neither parallel nor perpendicular.