## help_people one year ago @mathstudent55

1. help_people

Select the equations that are parallel and perpendicular to y = 2x - 1 and that pass through the point (4, 1). parallel: y = 2x - 7 perpendicular: y = negative one over twox + 3 parallel: y = 2x + 2 perpendicular: y = negative one over twox + four and one half parallel: y = negative one over twox - 7 perpendicular: y = 2x + 3 parallel: y = -2x - 7 perpendicular: y = negative one over twox - 1

2. help_people

i think it is a

3. help_people

@mathstudent55

4. help_people

@mathmate @mathmath333

5. anonymous

a is the first set of choices?

6. mathmath333

u should write the options properly to make them more understandable particularly the perpendicular lines

7. help_people

ok

8. help_people

hold on

9. help_people

a:$y=2x-7$

10. help_people

|dw:1433696367134:dw|

11. help_people

|dw:1433696418674:dw|

12. mathstudent55

@help_people Do you know the relationship of the slopes of two parallel lines? Do you know the relationship of the slopes of two perpendicular lines?

13. help_people

parallel lines have asme slope different y-intercepts

14. mathstudent55

Correct.

15. help_people

to ahnge to perpinduculat make the slope negative and the reciprocal?

16. mathstudent55

Correct.

17. help_people

reciprocal is like 4/1 changef to 1/4

18. mathstudent55

Yes.

19. help_people

i am sure you know that was just in case you were going to sake me :D

20. help_people

21. help_people

is a correct? i know that c and d are not correct

22. help_people

because of them for parallel they do not have the asme slope

23. mathstudent55

Let's work on the parallel line first. Given line: $$y = 2x - 1$$ General equation of line in slope-intercept form: $$y = mx + b$$ A parallel line has the same slope as the given line. We need a line with slope 2.

24. mathstudent55

The parallel line has to have an equation of the form $$y = 2x + b$$ since we know its slope must be 2 just like the given line. We are given point (4, 1), so let's plug in (4, 1), and find b. $$1 = 2(4) + b$$ What do you get for b?

25. help_people

1=6+b -6 -6?

26. mathstudent55

2 * 4 = 8, not 6.

27. help_people

-8 srry than b=-7?

28. mathstudent55

Then subtract 8 from both sides.

29. mathstudent55

Yes. Since we now have b = -7, the parallel line is: $$y = 2x - 7$$

30. mathstudent55

Now we can work out the perpendicular line in a similar way.

31. mathstudent55

Now for the perpendicular line. Given line: $$y=2x−1$$ General equation of line in slope-intercept form: $$y=mx+b$$ Perpendicular lines have slopes that are negative reciprocals of each other. The given line has slope 2. What is the negative reciprocal of 2?

32. help_people

-1/2?

33. mathstudent55

Correct. We now insert the new slope in the slope-intercept form. $$y = -\dfrac{1}{2}x + b$$ Now we insert the know point on the line and solve for b.

34. mathstudent55

$$y = -\dfrac{1}{2}x + b$$ $$1 = \left( -\dfrac{1}{2} \right) (4) + b$$ What is b?

35. help_people

3

36. mathstudent55

Great. The equation of the perpendicular line is: $$y = -\dfrac{1}{2} x + 3$$

37. mathstudent55

Now choose the correct choice from the answers.

38. help_people

is still say a @mathstudent55

39. mathstudent55

40. help_people

ty

41. mathstudent55

yw