Which is the graph of 3y – 5x ≤ –6?

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Which is the graph of 3y – 5x ≤ –6?

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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I think it C the 3rd one
  • phi
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.

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Other answers:

  • phi
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)
  • phi
remember \( \le\) means solid line. cross off the choices that use dashed lines.
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
Thats why I said the 3rd one
  • phi
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 ?
this sound like I'm not smart but, do we plug in 0,0 for and y
and x
  • phi
yes.
ok about to work it out, just a sec
ok that leads t 3-5
  • phi
what you do is replace x with 0 and y with 0 3y – 5x ≤ –6 3*0 - 5*0 <= -6 ?
  • phi
then order of operations: first the multiply 3*0=0 5*0 = 0 0 - 0 <= - 6? 0 <= -6 ? true or false?
false
  • phi
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
Would I always change to symbol when solving inequalities?
  • phi
can you ask that a different way?
I noticed that instead of the symbol being less than or equal to its just< now?
  • phi
I was using <= to show how to type it if you can't type \( \le\)
oh okay, sorry. I learned something about if you divide change the symbol. making sure it wasn't this sorry
  • phi
first, can you choose the correct answer? solid line, origin not shaded.
A the first one
  • phi
yes
Thanks so much, I'll apply what you taught me in my other problems, hopefully I'll get them right. Thanks so much
I see your typing, didn't see that
  • phi
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
okay, Much understood Thinks for clarifying that for me
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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