Question

Which is the graph of 3y – 5x ≤ –6?

Answer 1

I think it C the 3rd one

Answer 2

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.

Answer 3

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)

Answer 4

remember \( \le\) means solid line. cross off the choices that use dashed lines.

Answer 5

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

Answer 6

Thats why I said the 3rd one

Answer 7

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 ?

Answer 8

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

Answer 9

and x

Answer 10

yes.

Answer 11

ok about to work it out, just a sec

Answer 12

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.

Answer 13

what you do is replace x with 0 and y with 0
3y – 5x ≤ –6
3*0 - 5*0 <= -6 ?

Answer 14

then order of operations: first the multiply
3*0=0
5*0 = 0
0 - 0 <= - 6?
0 <= -6 ?
true or false?

Answer 15

false

Answer 16

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

Answer 17

Would I always change to symbol when solving inequalities?

Answer 18

can you ask that a different way?

Answer 19

I noticed that instead of the symbol being less than or equal to its just< now?

Answer 20

I was using <= to show how to type it if you can't type \( \le\)

Answer 21

oh okay, sorry. I learned something about if you divide change the symbol. making sure it wasn't this sorry

Answer 22

first, can you choose the correct answer? solid line, origin not shaded.

Answer 23

A the first one

Answer 24

yes

Answer 25

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

Answer 26

I see your typing, didn't see that

Answer 27

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

Answer 28

okay, Much understood Thinks for clarifying that for me

Answer 29

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