Question

Determine whether the graphs of the given equations are parallel, perpendicular, or neither

Answer 1

Keywords

parallel, perpendicular, graphing, linear equation, slope, lines

we know that

If two lines are perpendicular, then the product of their slope is equal to minus one

so

$m1*m2=-1$

If two lines are parallel, then their slope are equal

$m1=m2$

In this problem we have

$y=x+11$ --------> linear equation A

the slope is $m1=1$

$y=-x+2$  --------> linear equation B

the slope is $m2=-1$

Find the product

$m1*m2=-1$ ---------> the lines are perpendicular

therefore

the answer is the option B

Perpendicular

using a graphing tool

see the attached figure

Answer 2

Answer:

Perpendicular

Step-by-step explanation:

Given are two equations as

$y=x+11\\y=-x+2$

We have to find whether these two are parallel or perpendicular or neither

For this first we have to find the slope of these two lines

I line slope = 1

II line slope =-1

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

Let us check product of these slopes.  IF product =-1 the lines are perpendicular

We find that product = $1*-1=-1$

Hence two lines are perpendicular