## DaniSchwarz 2 years ago Given two points on the line, input the equation of the line in standard form Ax + By = C. Reduce all fractional answers to lowest terms. (7, -3), (4, -8)

1. myininaya

Well we can put into y=mx+b form first then rearrange it to the standard form. So m represents slope and b is the y-intercept. Given two points, you can use the slope formula which is (x1-x2)/(y1-y2)

2. DaniSchwarz

So (7-4)/(-3-(-8)?

3. myininaya

oops i put my x's on top. (y1-y2)/(x1-x2)

4. DaniSchwarz

Ok so (-3-(-8)/(7-4)?

5. myininaya

yes (-3-(-8))/(7-4) Do the subtraction on top and then do the subtraction on bottom.

6. DaniSchwarz

So 5/3

7. myininaya

yes that is m, the slope so let's fill in the info we have y=5x/3+b The only thing we don't know now is b, the y-intercept. you can use a point on the line (either of the two given to you) to find b. So if we use (7,-3) then we will see we have only one know in the following equation -3=5(7)/3+b Solve for b.

8. DaniSchwarz

So -3*3=5(7)/3*3+b = 9=35+b?

9. myininaya

Well if you are multiplying both sides by 3 to get rid of that fraction then you can't forget to multiply each term on the right hand side by 3. So you should have -3*3=5(7)/3*3+3*b

10. myininaya

-9=35+3b

11. DaniSchwarz

Ok. So next I need to get 3b on the left side right?

12. myininaya

Well you could leave it on the right and do something with that 35 instead but yeah either way really.

13. DaniSchwarz

Okay so -9 - 35 = 35 - 35 +3b?

14. myininaya

yep yep

15. DaniSchwarz

Okay so -44 = 3b?

16. myininaya

yep

17. DaniSchwarz

And then -44/3 = 3b/3 which equals -14 2/3 =3b?

18. myininaya

Yes I would leave it just in the improper form. So we have m=5/3 and b=-44/3 This means y=mx+b ---> y=5x/3-44/3

19. myininaya

We should be able to rearrange this into the form you want Ax+By=C

20. DaniSchwarz

So 5x/3+y=-44/3?

21. myininaya

Did you subtract 5x/3 on both sides? Looks like you subtracted on one side but not the other.

22. DaniSchwarz

So -5x/3+y=-44/3?

23. myininaya

Yes. Now get rid of fractional part by multiplying both sides by 3 and you are done.

24. DaniSchwarz

So -5x + y = -44?

25. myininaya

You need to also multiply that one term by 3.

26. myininaya

3(-5x/3+y=-44/3) 3(-5x/3+y)=3(-44/3) 3(-5x/3)+3(y)=3(-44/3) -5x + 3y = -44

27. DaniSchwarz

Ohh! Alright! Thank you!

28. myininaya

You did good. Good job Dani.