## anonymous one year ago A line passes through the point (–3, –4) and its y-intercept is (0, –9). What is the equation of the line that is parallel to the first line and passes through the point (3, –7)?

|dw:1437711431685:dw| First find the Slope of the First Line using the formula: Slope, m = (y2-y1)/(x2-x1) The slope of second line and first line will be Equal. Because parallel lines have equal slope. once you get the slope of second line, the equation can be written : y - y1 = m(x - x1)

|dw:1437711852579:dw|

3. anonymous

im not sure i understand

4. JoannaBlackwelder

Can you find the slope of the first line?

5. anonymous

im confused with the whole thing, i dont understand any of it

6. JoannaBlackwelder

Ok, are you familiar with this formula? |dw:1437712598401:dw|

7. JoannaBlackwelder

Where m is slope of a line

8. anonymous

yes!

9. JoannaBlackwelder

Great! :-) Can you plug in the two points given for the first line to find the slope?

10. anonymous

do you mean (-3,-4) & (0,-9) ?

11. JoannaBlackwelder

Yep

12. anonymous

is it y=5/3x-2 ?

13. JoannaBlackwelder

Hm, I get the slope to be -5/3|dw:1437713469475:dw|

|dw:1437713498055:dw| this is what @JoannaBlackwelder tried to say... you need to susbstitute the values of x1, x2, y1, y2

15. JoannaBlackwelder

And the slope of parallel lines is equal. :-)

16. JoannaBlackwelder

So, the slope of the other line is also -5/3. Making sense so far?

17. anonymous

was i close ?

18. JoannaBlackwelder

Yes, but your slope was off.

19. JoannaBlackwelder

Any ideas on finding the equation of the second line, using the slope of -5/3 and the point (3,-7)

20. anonymous

okay one question, if a slope of a line is -1/2 the slope that is parallel to it would be -2 right?

21. anonymous

or would it be just 2?

22. JoannaBlackwelder

Parallel lines have the exact same slope

23. anonymous

so it would be -1/2 ?

24. JoannaBlackwelder

Right.

25. JoannaBlackwelder

Perpendicular lines have negative reciprocal slopes is what I think you were thinking about before.

26. anonymous

could you help with this one as well? The equation of a line is y = 2x + 3. What is the equation of the line that is parallel to the first line and passes through (2, –1)?

27. JoannaBlackwelder

Sure, can you tell what the slope of the line given is?

28. anonymous

m=2x ?

29. JoannaBlackwelder

Close, just the 2 is the slope.

30. JoannaBlackwelder

Now, we need to use that slope since the lines are parallel and the point (2,-1) to find the new equation of the line.

31. anonymous

okay how do i set up the equation?

32. JoannaBlackwelder

We use the general formula y=mx+b

33. JoannaBlackwelder

Plug in m, and the x and y coordinate we have

34. JoannaBlackwelder

|dw:1437716031316:dw|

35. JoannaBlackwelder

And solve for b

36. JoannaBlackwelder

Can you find b?

37. anonymous

2(2) would turn into 4x right? would i then divide that by -1 to get b?

38. JoannaBlackwelder

Close

39. JoannaBlackwelder

|dw:1437716846824:dw|

40. JoannaBlackwelder

|dw:1437716867087:dw|

41. JoannaBlackwelder

Make sense?

42. anonymous

Yes ! that make sense!

43. JoannaBlackwelder

Awesome! So then we can plug in m and b to make y=2x+(-6)

44. JoannaBlackwelder

or y=2x-6

45. anonymous

right !

46. JoannaBlackwelder

:-D

47. anonymous

thank you so much !!

Find more explanations on OpenStudy