## anonymous 5 years ago Find the equation of the line perpendicular to the line containing (-2, 4) with slope zero, going through (-2, 4). What's the slope? I'm confused.

1. anonymous

Hehe...draw it.

2. anonymous

First line goes through (-2,4) and is horizontal. Second line goes through the same point and is perpendicular (i.e. vertical). It's slope is 'infinity'.

3. anonymous

4. anonymous

The slope is defined as$m=\frac{y_2-y_1}{x_2-x_1}$For the horizontal line, you have that it has the same y-value for ANY x value, so the slope is$m=\frac{y-y}{x_2-x_1}=\frac{0}{x_2-x_1}=0$but

5. anonymous

for the second line, the vertical one, it has the same x-value for ALL y-values, so you end up with$m=\lim_{x_0 \rightarrow x}\left| \frac{y_2-y_1}{x_0-x} \right|=\infty$

6. anonymous

because you end up dividing by zero (just put numbers into your calculator where you hold the numerator fixed and let the denominator get closer and closer to zero, and you'll see the result gets larger and larger.

7. anonymous

My first equation I have is y=4 which is horizontal right? How do I make my second equation to show what you are showing me?

8. anonymous

x=-2

9. anonymous

x=-2 means, "x is -2 for all y".

10. anonymous

Oh okay, this is the case because both of the points are the same, correct?

11. anonymous

Which points are you talking about?

12. anonymous

Both lines share only one point. The horizontal line has different x for same y. The vertical has same x for different y.

13. anonymous

it seems it is only asking for one slope? You are getting two aren't you?

14. anonymous

You're being asked for the slope of the line perpendicular to the line with slope zero. This perpendicular line is the vertical one, and it has the (technically undefined, and therefore non-existent) slope of infinity.

15. anonymous

Look at what I'm about to send.

16. anonymous
17. anonymous

18. anonymous

The slope of the line is also the tan of the angle subtended between the positive x-axis and the line (i.e. tan(theta) since by definition of tan, tan is opposite over adjacent). The tan function 'blows up' as you go to theta = 90 degrees...plot it...check it out. Use wolframalpha.com or download this free software: http://www.geogebra.org/cms/

19. anonymous

well we have not really got that far, I appreciate your help. I understand a lot better. So basically the equation of the line is y=4? because you also have x=-2 and it says THE so he is only asking for one.

20. anonymous

SOOO the equation of the line perpendicular is x=-2 while the slope does not exist or is infinite. Right?

21. anonymous