Determine whether if lines are parallel or perpendicular

Question

y+8=-6x, -2x+y=5

Answer 1

Hi Wanda,

 

Let's write the equations in slope-intercept form, i.e., y = mx + b

y + 8 = -6x

y = -6x - 8

 

-2x + y = 5

y = 2x + 5

 

Two lines will be parallel if their slopes are the same, i.e., m1 = m2, and perpendicular if their slopes have the following relationship

m1 = -1/m2

So, let's consider the slopes of our equations. The first line has a slope of m1 = -6

The second line has a slope of m2 = 2

The slopes are neither equal to each other nor have the relationship m1 = -1/m2. therefore they are neither parallel nor perpendicular. 

Answer 2

y = -6x - 8

y = 2x + 5

 

In order to be parallel, the lines have to have the same slope. In order to be perpendicular, the lines have to have opposite, reciprocal slopes.