Question

1. Which point on the axis satisfies the inequality y

- (0,1)
- (-1,0)
- (1,0)
- (0,0)


2. I the graph of the inequality x-2y>=4, which is a value for x on the boundary line and the x axis?

- 4
- -2
- 2
- -2


3. If x >=0 and y>=0, then which quadrant holds the solution?

- IV
- III
- I
- II


4. Which ordered pair is a solution of the inequality?
y>=4x-5

- (3,4)
- (2,1)
- (3,0)
- (1,1)


5. Write an inequality to match the graph.

- y<-5x+3
- y>5x+3
- y<5x+3
- y>-5x+3

Answer 1

1.) C - (1, 0)
2.) A - 4
3.) C - 1
4.) D - (1, 1)
5.) D

Answer 2

1) Point
`(1,0)` -----> see the attached figure N
`1`

2) The value of x is
`4`

3) I quadrant

4)
`(1,1)`

5)
`y>-5x+3`

Explanation:

Part 1)

we know that

If the point satisfy the inequality

then

the point must be included in the shaded area

The point
`(1,0)` is included in the shaded area

Part 2)

we have

`x-2y\geq 4`

see the attached figure N
`2`

we know that

The value for x on the boundary line and the x axis is equal to the x-intercept of the line
`x-2y= 4`

For
`y=0`

Find the value of x

`x-2(0)= 4`

`x=4`

The solution is
`x=4`

Part 3)

we have

`x\geq 0` -----> inequality A

The solution of the inequality A is in the first and fourth quadrant

`y\geq 0` -----> inequality B

The solution of the inequality B is in the first and second quadrant

so

the solution of the inequality A and the inequality B is the first quadrant

Part 4) Which ordered pair is a solution of the inequality?

we have

`y\geq 4x-5`

we know that

If a ordered pair is a solution of the inequality

then

the ordered pair must be satisfy the inequality

we're going to verify all the cases

case A) point
`(3,4)`

Substitute the value of x and y in the inequality

`x=3,y=4`

`4\geq 4(3)-5`

`4\geq 7` ------> is not true

therefore

the point
`(3,4)` is not a solution of the inequality

case B) point
`(2,1)`

Substitute the value of x and y in the inequality

`x=2,y=1`

`1\geq 4(2)-5`

`1\geq 3` ------> is not true

therefore

the point
`(2,1)` is not a solution of the inequality

case C) point
`(3,0)`

Substitute the value of x and y in the inequality

`x=3,y=0`

`0\geq 4(3)-5`

`0\geq 7` ------> is not true

therefore

the point
`(3,0)` is not a solution of the inequality

case D) point
`(1,1)`

Substitute the value of x and y in the inequality

`x=1,y=1`

`1\geq 4(1)-5`

`1\geq -1` ------> is true

therefore

the point
`(1,1)` is a solution of the inequality

Part 5) Write an inequality to match the graph

we know that

The equation of the line has a negative slope

The y-intercept is the point
`(3,0)`

The x-intercept is a positive number

The solution is the shaded area above the dashed line

so

the equation of the line is
`y=-5x+3`

The inequality is
`y>-5x+3`