Question

Determine if the following lines are parallel, perpendicular, or neither. y=x-8 x+y=-5

Answer 1

Answer: Perpendicular

Explanation:

Our task is to identify if these lines are parallel or not. The lines are :

• 
  `\rm{y=x-8}`
• 
  `\rm{x+y=-5}`

A good move would be to write these two equations in the same format. The easiest one is slope-intercept. Equation 1 is already in this form, but the second one isn't.

To write the second equation in slope-intercept, all we need to do is subtract x from both sides, and we get:

• 
  `\rm{y=-5-x}`

Now, switch the terms:

• 
  `\rm{y=-x-5}`

The slope of the first line is 1, and the slope of the second line is -1.

They can't be parallel, since their slopes are not the same. For them to be perpendicular, their slopes should be negative reciprocals of each other.

Is -1 the negative inverse of 1? Yes.

∴ The lines are perpendicular.

Answer 2

To determine if two lines are parallel or perpendicular, we need to examine their slopes.

First, let's rearrange the second equation, x+y=-5, to slope-intercept form (y = mx + b):

y = -x - 5

In this form, we can see that the slope of the second line is -1.

The first equation, y=x-8, is already in slope-intercept form, y = mx + b, where the slope is 1.

Comparing the slopes, we can see that the slopes of the two lines are different. The slope of the first line is 1, and the slope of the second line is -1.

Since the slopes are not equal, the lines are not parallel.

Now, let's determine if the lines are perpendicular:

Two lines are perpendicular if the product of their slopes is -1.

The slope of the first line is 1, and the slope of the second line is -1.

Since 1 * -1 = -1, the product of the slopes is -1.

Therefore, the lines y = x - 8 and x + y = -5 are perpendicular.

Explanation: