Which best describes the relationship between the two lines described below?

linep: 6x+3y=12

line q: -4x=2y-2

answer choices:

a. perpendicular

b. parallel

c. same line

d. neither parallel nor perpendicular

b. Parallel

Step-by-step explanation

Hello! To help solve this problem, you must first be able to familiarize yourself with the concept of parallel and perpendicular lines.

A pair of line equation can be considered parallel if their slope(m) is equal. On the other hand, a pair of line equation can be considered perpendicular if their slope(m) is the negative reciprocal of each other.

Now, for this problem, we will try to identify the slope of each equation. We will try to arrange each equation in it's slope-intercept form, like this

y = mx + b

where m is the slope

For line p, we have:

6x+3y=12

Rearranging this, we have

6x+3y = 12

3y = -6x+12

y = ?3−6x+12??

y = -2x + 4

For this, m₁ = -2

For line q, we have:

-4x=2y-2

Rearranging this, we have

-4x=2y-2

2y = -4x+2

y = ?2−4x+2??

y = -2x+1

For this, m₂ = -2

Now, since both slope of the two lines are equal, we can therefore conclude that the lines are parallel to each other.

If we try to graph this using the aid of a graphing calculator, the lines would look like this,

Please see the attached file for the complete solution