Question

Determine whether the origin is included in the shaded region and whether the shaded region is above or below the line for the graph of the following inequality:

y > three fifthsx − 2

The origin is not included in the shaded region and the shaded area is above the line.
The origin is not included in the shaded region and the shaded area is below the line.
The origin is included in the shaded region and the shaded area is above the line.
The origin is included in the shaded region and the shaded area is below the line.

Answer 1

@queen-of-tokyo

Answer 2

@WhateverYouSay

Answer 3

@sweetburger

Answer 4

@zepdrix

Answer 5

@yomamabf

Answer 6

Hey there :)
Let's answer the second part of the question first, because it's really simple.

Answer 7

When you have something like this:
\(\large\rm y\lt \color{orangered}{2x+3}\)
Think of it like this:
\(\large\rm y\lt \color{orangered}{\text{the line}}\)
The orange part represents the line.
So in this example,
we want all of the `y values` which are `less than` `the line`.
So in this example we would shade `below` the line.

Answer 8

How bout in your problem?

y is GREATER THAN some line.
So where we gonna shade?

Answer 9

above the line correct? @zepdrix

Answer 10

k good :) that already narrows down our choices!

Answer 11

\[\large\rm y\gt\frac{3}{5}x-2\]Recall that the origin is the point (0,0).
So let's just plug it in...
and find out if the inequality holds true!

Answer 12

\[\large\rm 0\gt\frac{3}{5}\cdot0-2\]After you simplify this a bit,
does the inequality hold true?

Answer 13

no

Answer 14

its the same right?

Answer 15

So after simplifying, we have, 0 > -2

Answer 16

Hmm that appears to hold true, ya?
0 is larger than -2

Answer 17

oh yes my bad i was looking at the wrong thing

Answer 18

Ok good!
So we figured out that the point (0,0) DOES in fact satisfy our inequality.
So it is included in the shaded area.

Answer 19

thanks could you help mw with one more

Answer 20

sure, i can try :)

Answer 21

Given the system of equations presented here:

3x + 5y = 29
x + 4y = 16

Which of the following actions creates an equivalent system such that, when combined with the other equation, one of the variables is eliminated?

Multiply the second equation by −1 to get −x − 4y = −16
Multiply the second equation by −3 to get −3x − 12y = −48
Multiply the first equation by −1 to get −3x − 5y = −29
Multiply the first equation by −3 to get −9x − 15y = −87

Answer 22

You're trying to match up the coefficients on either the x's or the y's, but not both.
If we wanted to match up the x's, maybe we would need some kind of 3.

If we wanted to match up the y's, it would be a little more difficult.
We would multiply the first equation by 4,
and the second equation by -5.
They would then both have coefficients of 20, one of them being negative.
So they would combine nicely.

They didn't do that here though.
They went the easier route.
They're matching up the x's somehow.

Answer 23

We want them to match.
Notice the first equation already has a 3, so it doesn't need anything more.

Answer 24

So what do you wanna do to the second equation to match them up?

Answer 25

add a 1 to the x?

Answer 26

The first equation has 3x.

The second equation has x.
If we add 1 to x, hmm I'm not really sure what that will do for us :d
We want the same number of x in both equations.

Answer 27

We don't want to add.
We want to multiply that second equation by some number that will turn it from x to some kind of 3x.

Answer 28

you would multiply it by 3 then

Answer 29

@zepdrix

Answer 30

Good good good, we would multiply the second equation 3!
That would give us 3x.

But in order for them to combine, and disappear, we want one of them to be negative.
So let's instead multiply the second equation by negative 3.

Answer 31

boom bam! yay team!

Answer 32

so the answer is D yes? @zepdrix

Answer 33

Option D talks about changes to equation 1.
We were making changes to equation 2.

Answer 34

oh ok i wasn't reading carefully but thank you for your help :) @zepdrix