## anonymous 2 years ago Help with these:/ I don't understand

1. anonymous

2. hartnn

can you find slope of any given line ?

3. hartnn

like say , x-5y = -10 is a line. can you find slope of this line first ?

4. anonymous

Uh no not really... with a quick review I probably can

5. hartnn

good, so i have x-5y =-10 i will try to isolate y and bring it in the form y=mx+c where m=slope so, x=5y-10 5y = x+10 y= (1/5)x +2 got this ?

6. anonymous

Yeah I got it

7. hartnn

cool, so can you find the slope of x -3y=9 line ? in same way

8. hartnn

oh and i forgot to mention, y= (1/5)x +2 comparing with y=mx+c gives, m=slope = 1/5

9. anonymous

x-37=9 -3y=x+9 Y=(1/3)x+3

10. anonymous

So slope would be 1/3 I assume?

11. hartnn

correct! :) now try to find slopes of other 3 lines also! and tell me, so that i will verify :)

12. anonymous

4x+2y=5 2y=-4x+5 Y-(-1/2)x+2.5 ?

13. hartnn

2y=-4x+5 is correct, but then divide both sides by 2 what u get ?

14. anonymous

10x-5y=8 -5y=10x+8 Y=-2x+1.6?

15. hartnn

10x-5y=8 -5y=10x+8 <<<<<<NO! -5y = -10x +8

16. anonymous

and you would get y=-2+2.5

17. anonymous

Ahh okay -10 so the problem would come out with a positive 2x

18. hartnn

yes, so the slope will be m= 2 , right ?

19. anonymous

Yes

20. hartnn

4x+2y=5 slope = -2 make a note of all slopes, we'll need them

21. hartnn

and what about last line ?

22. anonymous

4x+y=-1 Y=-4x-1

23. hartnn

so, slope =?

24. anonymous

-4

25. hartnn

Good! now here's the rule : slope of parallel lines are equal! so, for the last one, slope of line parallel to 4x+y=-1 will also be m=-4 :) so, for last, the correct option will be C) m=-4 got this ? in same way, can you match the 2nd last and 3rd last ?

26. anonymous

Yeah I got it, Thanks a ton man. You need to be my teacher xD

27. hartnn

haha, :) but we still require to do the 1st 2 !

28. hartnn

another rule, product of slopes of perpendicular lines = -1  so, for 1st one we had slope = 1/5 let slope of perpendicular line be m. so, $$\Large m\times (1/5)=-1$$ find m from here :)

29. anonymous

1st one is m=1/5? 2cnd one is m=1/3? It seems like these would be the answers but they are not possible to be selected.

30. anonymous

Ahhhh okay

31. hartnn

because perpendicular lines follow different rule :)

32. anonymous

Well I still don't exactly get how it goes from (1/5) to -1...

33. hartnn

product of slopes = -1 is the rule so, m (1/5) =-1 multiplying by 5, m = -5 got this ?

34. hartnn

multiplying by 5 on both sides.

35. anonymous

I'm confused on the product of slopes part, I get the multiplying on both sides. So like can you explain the product of slopes rule.. I tried looking it up on google but nothing I can comprehend really comes up.

36. hartnn

if say line 1 has slope M1 and line 2 has slope M2 now if these 2 lines are perpendicular to each other, then M1*M2 =-1

37. hartnn

another way to remember the same thing is, the slope of line is negative reciprocal of the perpendicular line, so, slope of line perpendicular to line with slope 1/5 will be - (1/(1/5)) = -5

38. hartnn

so, thats your 1st one, m =-5 for 2nd one, we had slope = 1/3, so m *(1/3) = -1 so, m=-3 is the answer to 2nd one :)

39. anonymous

Okay, so basically whenever there is a fraction just take (1/_) blank space number lol

40. hartnn

you forgot the negative :P -1/ stuff

41. hartnn

but this only applies to perpendicular lines

42. hartnn

for parallel lines, slope are equal

43. anonymous

Oh I see says the blind man

44. hartnn

what who ?

45. hartnn

lol

46. hartnn

i hope you got the entire problem clearly ?

47. hartnn

48. anonymous

Yeah I get it now man thanks a ton

49. hartnn

welcome ^_^