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freemap

  • one year ago

Which is the graph of 3y – 5x ≤ –6?

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  1. freemap
    • one year ago
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  2. freemap
    • one year ago
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    I think it C the 3rd one

  3. phi
    • one year ago
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    I would add 5x to both sides 3y - 5x + 5x <= 5x-6 \[ 3y \le 5x -6 \] then divide both sides by 3 \[ y \le \frac{5}{3}x -6 \] the equal part of the \( \le\) means we use a solid line (if it wer \( \lt \) , it would be a dashed line) when x=0, y is -6 so look for a line that goes through (0,-6) the slope is 5/3 which means up 5 and over 3 \( y \le stuff \) means we want the y values that are "under" the line an easy way to decide is put in (0,0) into the original equation 3y – 5x ≤ –6 0 <= -6 no. so the side without the origin is the side we want.

  4. phi
    • one year ago
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    after typing all that I see I did not divide correctly it should be \[ y \le \frac{5}{3}x - 2 \] so the line goes through (0,-2) (not (0,-6) as I wrote up above)

  5. phi
    • one year ago
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    remember \( \le\) means solid line. cross off the choices that use dashed lines.

  6. freemap
    • one year ago
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    since the symbol is less than or equal to the line is solid not dashed and since its less than it goes up to that point and all the way to the left thats what I learned

  7. freemap
    • one year ago
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    Thats why I said the 3rd one

  8. phi
    • one year ago
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    now check if the origin is on the true (shaded ) side of the line. 3y – 5x ≤ –6 when we use (0,0) what do we get ?

  9. freemap
    • one year ago
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    this sound like I'm not smart but, do we plug in 0,0 for and y

  10. freemap
    • one year ago
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    and x

  11. phi
    • one year ago
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    yes.

  12. freemap
    • one year ago
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    ok about to work it out, just a sec

  13. freemap
    • one year ago
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    ok that leads t 3-5</ -6 or it doesn't The line goes with the symbol don't know how to do line under it.

  14. phi
    • one year ago
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    what you do is replace x with 0 and y with 0 3y – 5x ≤ –6 3*0 - 5*0 <= -6 ?

  15. phi
    • one year ago
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    then order of operations: first the multiply 3*0=0 5*0 = 0 0 - 0 <= - 6? 0 <= -6 ? true or false?

  16. freemap
    • one year ago
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    false

  17. phi
    • one year ago
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    so (0,0) is on the "wrong side" we shade the "correct side" which in this case is the side that does not have the origin

  18. freemap
    • one year ago
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    Would I always change to symbol when solving inequalities?

  19. phi
    • one year ago
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    can you ask that a different way?

  20. freemap
    • one year ago
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    I noticed that instead of the symbol being less than or equal to its just< now?

  21. phi
    • one year ago
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    I was using <= to show how to type it if you can't type \( \le\)

  22. freemap
    • one year ago
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    oh okay, sorry. I learned something about if you divide change the symbol. making sure it wasn't this sorry

  23. phi
    • one year ago
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    first, can you choose the correct answer? solid line, origin not shaded.

  24. freemap
    • one year ago
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    A the first one

  25. phi
    • one year ago
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    yes

  26. freemap
    • one year ago
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    Thanks so much, I'll apply what you taught me in my other problems, hopefully I'll get them right. Thanks so much

  27. freemap
    • one year ago
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    I see your typing, didn't see that

  28. phi
    • one year ago
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    the "change the symbol" rule happens if you *multiply or divide by a negative number* you can get around that rule by *never* multiplying or dividing by a negative number say you have -x < 2 if we multiply both sides by -1 we get -1*-x > -1*2 x > -2 (we changed the direction of the sign) but we could do this: add +x to both sides -x+x < 2+x 0 < 2 + x now add -2 to both sides -2 < x we get the correct relation , which can also be written x> -2

  29. freemap
    • one year ago
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    okay, Much understood Thinks for clarifying that for me

  30. freemap
    • one year ago
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    Thanks so much, I'll apply what you taught me in my other problems, hopefully I'll get them right. Thanks so much

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