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## kenneyfamily 2 years ago distance between lines? 6x - 8y = 3 6x - 8y = -5

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1. Hero

Hint: Use the distance formula for lines

2. ChmE

$\large d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

3. ChmE

That is for points

4. Hero

There's two ways to do it. You can either use the distance formula for LINES (yes there is such a thing) or you can find the line perpendicular to both given lines since they are parallel.

5. Hero

It's just a formula bro. It's nothing to get overly eager and excited about.

6. kenneyfamily

ok the question is the distance is 4/5. true or false?

7. Hero

The formula is $d = \frac{|ax + by + c|}{\sqrt{a^2 + b^2}}$ Where (x,y) is a point on one of the lines and a, b, c are the coefficients of the other line.

8. Hero

And I should say that this is specifically the formula for the distance between two PARALLEL lines.

9. RadEn

8/10 = 4/5 correct

10. Hero

(x,y) = (.5,0) is a point on the first given line. So use a = 6, b = -8, c = 5 for the other one.

11. Hero

Are you happy @ChmE ?

12. kenneyfamily

how would you non parallel lines? @Hero such as x + y - 1 = 0 and y = -x + 6

13. Hero

If the lines are not parallel, then the distance between them would not be consistent.

14. Hero

That formula I gave you (as I stated previously) is for PARALLEL lines only

15. kenneyfamily

hmm but it is answerable

16. Hero

Well, actually, what you just posted are two parallel lines.

17. Hero

y = -x + 1 and y = -x + 6

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