Question

Are the lines - 6x + 3y = -9 and y + 1 = -3(x + 2) parallel,
perpendicular, or neither?

Answer 1

• Neither

Explanation:

Given lines:

• - 6x + 3y = -9 and
• y + 1 = -3(x + 2)

To determine the answer we need to compare slopes of the lines.

Parallel lines have same slopes, perpendicular lines have negative-reciprocal slopes.

Let's put them in slope-intercept form:

• - 6x + 3y = -9 ⇒ -2x + y = - 3 ⇒ y = 2x - 3
• y + 1 = -3(x + 2) ⇒ y + 1 = -3x - 6 ⇒ y = -3x - 7

As we see the slopes are 2 and -3, so the lines are neither parallel nor perpendicular