Which is the graph of 3y – 5x ≤ –6?

- freemap

Which is the graph of 3y – 5x ≤ –6?

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- freemap

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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## More 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.

- freemap

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

- freemap

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 ?

- freemap

this sound like I'm not smart but, do we plug in 0,0 for and y

- freemap

and x

- phi

yes.

- freemap

ok about to work it out, just a sec

- freemap

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?

- freemap

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

- freemap

Would I always change to symbol when solving inequalities?

- phi

can you ask that a different way?

- freemap

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 \( \le\)

- freemap

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.

- freemap

A the first one

- phi

yes

- freemap

Thanks so much, I'll apply what you taught me in my other problems, hopefully I'll get them right. Thanks so much

- freemap

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

- freemap

okay, Much understood Thinks for clarifying that for me

- freemap

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