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## anonymous 5 years ago Write an equation of the line containing the given point and parallel to the given line. (-2,8); 7x=5y+6

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1. shadowfiend

If two lines are parallel, what is the relation between their slopes?

2. anonymous

are they equal distance?. i dunno im horrible with math, not one of my strong points

3. shadowfiend

It's okay :) Two parallel lines have equal slopes. So, y = 3x + 135 y = 3x + 2 Those two are parallel lines, because they the same slope (3). Let's focus on the problem below, since you'll have to use the same technique to get the equation they give you in y = mx + b form here.

4. shadowfiend

So now you have 7x = 5y + 6. Since we need the slope, we need to solve for y again.

5. anonymous

okay so would we need to subtract 6 from both sides?

6. shadowfiend

Yep, that's the first step.

7. anonymous

-6+7x=5y

8. anonymous

or 5y=7x-6

9. shadowfiend

Right. What's next?

10. anonymous

get the y by itself

11. shadowfiend

Exactly. So since the y is multiplied by 5, how do we get it by itself?

12. anonymous

divide

13. shadowfiend

Right. So we divide each part of the right by 5; what do we get?

14. anonymous

y=7/5x-6/5

15. shadowfiend

Boom! Exactly. So now we know what the slope of a parallel line would have to be. What is it?

16. anonymous

7/5

17. shadowfiend

Right. So now we'll need another equation that looks like: y = 7/5x + b Does that make sense?

18. anonymous

yea that does

19. shadowfiend

Ok, and now they've given us a point that the line goes through, so we can plug in the x and y and solve for b.

20. anonymous

okay so 8=7/5(-2)+b

21. anonymous

is that right

22. anonymous

Absolutely!

23. anonymous

So now what do I do?

24. anonymous

So we need to figure out what b is, right? How should we do that?

25. anonymous

um get b by itself?

26. anonymous

Exactly. So what's the first step?

27. anonymous

multiply 7/5(-2)

28. anonymous

Ok, what does that equal?

29. anonymous

-6/5

30. anonymous

Not quite. Remember you are multiplying 7/5 by -2. Do you know how to multiply fractions?

31. anonymous

not really is it common denominators at all?

32. anonymous

That is actually for adding and subtracting. Multiplication is much easier. You are multiplying 7/5 by -2. Remember that -2 is the same as -2/1, which means you have $\frac{7}{5} \times \frac{-2}{1}$ then you just multiply straight across. What do you get?

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