Question

The graph below represents which system of inequalities?

y > 2x - 3
y > -x - 3

y < 2x - 2
y < -x + 3

y less than or equal to 2x - 2
y > -x + 3

None of the above

Answer 1

Do you know the intercept form?

\(\dfrac{x}{1} + \dfrac{y}{-2} = 1\)

\(\dfrac{x}{3} + \dfrac{y}{3} = 1\)

Putting those in Slope Intercept form might be a good way to go.

Answer 2

Observing that (0,0) is NOT in the solution set might be a good start.

Answer 3

What are the y intercepts of the two lines shown on the graph?

Answer 4

@Mertsj The solid line is -2. The other is 3.

Answer 5

So look at your first answer choice. Could that be the answer?

Answer 6

No.

Answer 7

What about the second choice? Is it a possibility so far?

Answer 8

Yes. So is the third choice.

Answer 9

Ok. Good. Now, the line with y intercept 3 is dotted. Does that fit either choice?

Answer 10

Yes, both choices.

Answer 11

The line with y intercept -2 is solid. Does that fit either choice?

Answer 12

The third one.

Answer 13

So now, we need to check the shading just in case the answer is "none of these"

Answer 14

Choice 3 says that the shading should be below the solid line. Is it?

Answer 15

Yes.

Answer 16

Choice 3 says that the shading should be above the dotted line. Is it?

Answer 17

Yes.

Answer 18

So choice 3 works and is the answer. Do you understand?

Answer 19

Yes, thank you. Have a nice day.

Answer 20

Good. You're welcome. Same to you.