Question

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

y= -1/4 x + 8
-2x + 8y = 4

Answer 1

Given equation are:

`y = -(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 = -(1)/(4)x+8`

then;

`m_1= -(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 = (1)/(4) x + (1)/(2)`

then;

`m_2 = (1)/(4)`

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