MEDAL AND FAN: HELP PLEASE!!!

Select the equations that are parallel and perpendicular to y = x + 5 and that pass through the point (-2, -1).

(Answer Choices):

A: Parallel y=-x-1
Perpendicular y=x+2

B: Parallel y=x-1
Perpendicular y=-x+1

C: Parallel y=x+1
Perpendicular y=-x-3

D: Parallel y=2x-2
Perpendicular y=-2x-1

I think it may be D?

Question

MEDAL AND FAN: HELP PLEASE!!!

Select the equations that are parallel and perpendicular to y = x + 5 and that pass through the point (-2, -1).

(Answer Choices): 

A: Parallel y=-x-1
Perpendicular y=x+2

B: Parallel y=x-1
Perpendicular y=-x+1

C: Parallel y=x+1
Perpendicular y=-x-3

D: Parallel y=2x-2
Perpendicular y=-2x-1

I think it may be D?

michele_laino · Answer

Hint:
parallel lines have the same slope
for example, here are two parallel lines:
$y=2x-3,\;\;\;\;y=2x+7$

anonymous · Answer

I'm confused ;-;

michele_laino · Answer

whereas, here are two perpendicular lines:
$y=2x+5,\;\;\;\;\; y=(-1/2)x-9$
as we can see the product of the slopes is:
$$\Large  2 \cdot \left( { - \frac{1}{2}} \right) =  - 1$$

michele_laino · Answer

in general, the equation slope-intercept of a line is:
$y=mx+q$, where $m$ is the slope

michele_laino · Answer

I think that option D is wrong

anonymous · Answer

Ah, ok. So its B? I think I understand. I'm sorry, math is my worst subject :/

michele_laino · Answer

let's consider option C, for example:
there the parallel line is: $y=x+1$, now I ask what is the slope of such line?

michele_laino · Answer

hint:
|dw:1454189692341:dw|

michele_laino · Answer

and the slope of the given line $y=x+5$ is also $1$, so such lines:
$y=x+1$, and $y=x+5$ are parallel lines

michele_laino · Answer

next: the slope of the line (option C) $y=-x-3$ is $-1$, and the product of that slope with the slope of the given line $y=x+5$, is:
$(-1) \cdot 1=-1$,
so the line $y=-x-3$ is perpendicular to the given line

anonymous · Answer

I'm sorry for the slow replies,answering other questions at the same time. I'm trying to get done with my exam before 12am haha but it's all so confusing.

michele_laino · Answer

now, the line $y=x+1$ passes at point $(-2,-1)$, since if I replace $x=-2$ into that equation, I get:
$y=-2+1=-1$

michele_laino · Answer

no problem :)

michele_laino · Answer

now, if I replace $x=-2$ into the equatiopn $y=-x-3$, I get:
$y=-(-2)-3=...?$ please continue

michele_laino · Answer

equation*

michele_laino · Answer

hint:
what is $-(-2)-3=...?$

anonymous · Answer

Wait so I was right?

michele_laino · Answer

no, since option D contains two lines whose slopes are not the right slopes

michele_laino · Answer

furthermore option B contain the lines $y=x-1$ which doesn't pass at point $(-2,-1)$

michele_laino · Answer

oops.. line*

anonymous · Answer

its c