Perpendicular lines help!!! Need to see if answers are correct!!

Question

anonymous · Answer

Let me post them:

anonymous · Answer

heres the first one

anonymous · Answer

2nd one

anonymous · Answer

@Astrophysics @phi @paki @Conqueror

anonymous · Answer

@mathmath333 @mathmate

igreen · Answer

y = x + 1

Do you know what the slope is here?

anonymous · Answer

the slope would be 1

igreen · Answer

Correct, and perpendicular lines have opposite slopes.

To find the slope of a perpendicular line, find the reciprocal of the slope and multiply it by -1.

Do you know how to find the reciprocal of a fraction?

Remember, $\sf 1 = \dfrac{1}{1}$

anonymous · Answer

reciprocal of a fraction would be flipping the numerator and denominator, correct?

igreen · Answer

Yep!

In this case, the numerator and denominator are the same.

anonymous · Answer

Okay! so are my answers incorrect?

igreen · Answer

No.

What's the reciprocal of $\sf \dfrac{1}{1}$?

anonymous · Answer

wouldn't the reciprocal of 1/1 be 1/1 since it's just flipping?

anonymous · Answer

of 1 sorry

anonymous · Answer

*or

igreen · Answer

Yep!

Now multiply it to -1 to find the slope of the perpendicular line.

anonymous · Answer

-1

igreen · Answer

Correct, so $\sf m = -1$

anonymous · Answer

ok! so how would i apply that to a question similar to this:

igreen · Answer

We just figured out the answer to that question.

anonymous · Answer

My bad, i meat #2

anonymous · Answer

*meant

igreen · Answer

For question #2, parallel lines have the same slope. So what's the slope of $\sf y = \dfrac{1}{2}x + 4$?

anonymous · Answer

the slope would be 1/2

igreen · Answer

Correct, so the slope of our new line is going to be 1/2.

Therefore, your answer is already wrong.

igreen · Answer

Now let's find the point that satisfies both equations $\sf y = 2x - 4$ and $\sf y = -x + 2$.

We can use substitution:

$\sf 2x - 4 = -x + 2$

Can you solve that for 'x'?

anonymous · Answer

the 'x' would be 2

igreen · Answer

Correct, now plug that into any of the two equations to find 'y'.

$\sf y = -2 + 2$

Simplify

anonymous · Answer

y would equal 0?

igreen · Answer

Yes..so our point is (2, 0) and our slope is 1/2.

Now plug this information into point-slope form.

$\sf y - y_1 = m(x - x_1)$

Where $\sf m$ is the slope and $\sf (x_1, y_1)$ is a point on the line.

Can you plug the information in?

anonymous · Answer

what would i put for the point on the line (x1, y1) if i only have (2, 0)

igreen · Answer

$\sf x_1 = 2$
$\sf y_1 = 0$

Plug these in along with $\sf m = \dfrac{1}{2}$.

anonymous · Answer

0-y1=1/2(2-x1)???

whpalmer4 · Answer

there is one important exception to the rule about finding the slope of perpendicular lines, and that is the case where you have a line of the form $$y=k$$ or $$x=k$$ where $k$ is a. constant.  The former has a slope of $0$ and the slope of the latter is undefined.  

To construct a perpendicular line to one of those, you just use the other form, with your choice of $k$ being determined by the point where they intersect.

For example, a line perpendicular to $x=3$ is going to be of the form $y=k$, where $k$ is the value of $y$ where the two lines intersect (and everywhere else).

anonymous · Answer

Wait okay: y-0=1/2(x-2)?

igreen · Answer

Correct, or:

$\sf y = \dfrac{1}{2}(x - 2)$

Now distribute 1/2 into the parenthesis.

igreen · Answer

Yes, that's correct @whpalmer4 

If you have a line with a slope of 0, the slope of the perpendicular line will be undefined, and vice versa.

anonymous · Answer

y=1/2x-1?

igreen · Answer

Yes! That's our answer.

anonymous · Answer

Oh, I see now! Thank you so much!

igreen · Answer

No problem.