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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)

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  1. myininaya
    • 2 years ago
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    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
    • 2 years ago
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    So (7-4)/(-3-(-8)?

  3. myininaya
    • 2 years ago
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    oops i put my x's on top. (y1-y2)/(x1-x2)

  4. DaniSchwarz
    • 2 years ago
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    Ok so (-3-(-8)/(7-4)?

  5. myininaya
    • 2 years ago
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    yes (-3-(-8))/(7-4) Do the subtraction on top and then do the subtraction on bottom.

  6. DaniSchwarz
    • 2 years ago
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    So 5/3

  7. myininaya
    • 2 years ago
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    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
    • 2 years ago
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    So -3*3=5(7)/3*3+b = 9=35+b?

  9. myininaya
    • 2 years ago
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    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
    • 2 years ago
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    -9=35+3b

  11. DaniSchwarz
    • 2 years ago
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    Ok. So next I need to get 3b on the left side right?

  12. myininaya
    • 2 years ago
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    Well you could leave it on the right and do something with that 35 instead but yeah either way really.

  13. DaniSchwarz
    • 2 years ago
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    Okay so -9 - 35 = 35 - 35 +3b?

  14. myininaya
    • 2 years ago
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    yep yep

  15. DaniSchwarz
    • 2 years ago
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    Okay so -44 = 3b?

  16. myininaya
    • 2 years ago
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    yep

  17. DaniSchwarz
    • 2 years ago
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    And then -44/3 = 3b/3 which equals -14 2/3 =3b?

  18. myininaya
    • 2 years ago
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    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
    • 2 years ago
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    We should be able to rearrange this into the form you want Ax+By=C

  20. DaniSchwarz
    • 2 years ago
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    So 5x/3+y=-44/3?

  21. myininaya
    • 2 years ago
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    Did you subtract 5x/3 on both sides? Looks like you subtracted on one side but not the other.

  22. DaniSchwarz
    • 2 years ago
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    So -5x/3+y=-44/3?

  23. myininaya
    • 2 years ago
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    Yes. Now get rid of fractional part by multiplying both sides by 3 and you are done.

  24. DaniSchwarz
    • 2 years ago
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    So -5x + y = -44?

  25. myininaya
    • 2 years ago
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    You need to also multiply that one term by 3.

  26. myininaya
    • 2 years ago
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    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
    • 2 years ago
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    Ohh! Alright! Thank you!

  28. myininaya
    • 2 years ago
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    You did good. Good job Dani.

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