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The coordinate plane below represents a city.

Points A through F are schools in the city. graph of coordinate plane. Point A is at negative 3, negative 4. Point B is at negative 4, 3. Point C is at 2, 2. Point D is at

The coordinate plane is below

Part A: Using the graph above, create a system of inequalities that only contain points C and F in the overlapping shaded regions. Explain how the lines will be graphed and shaded on the coordinate grid above.


Part B: Explain how to verify that the points C and F are solutions to the system of inequalities created in Part A.


Part C: Natalie can only attend a school in her designated zone. Natalie's zone is defined by y < −2x + 2. Explain how you can identify the schools that Natalie is allowed to attend.

The coordinate plane below represents a city. Points A through F are schools in the-example-1

1 Answer

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Answer:

Part A) The system of inequalities is


x\geq2 and
y\geq2

Part B) In the procedure

Part C) The schools that Natalie is allowed to attend are A,B and D

Explanation:

Part A: Using the graph above, create a system of inequalities that only contain points C and F in the overlapping shaded regions

we have

Points C(2,2), F(3,4)

The system of inequalities could be


x\geq2 -----> inequality A

The solution of the inequality A is the shaded area at the right of the solid line x=2


y\geq2 -----> inequality B

The solution of the inequality B is the shaded area above of the solid line y=2

see the attached figure N 1

Part B: Explain how to verify that the points C and F are solutions to the system of inequalities created in Part A

we know that

If a ordered pair is a solution of the system of inequalities, then the ordered pair must satisfy both inequalities

Verify point C

C(2,2)

Inequality A


x\geq2 ----->
2\geq2 ----> is true

Inequality B


y\geq2 ------>
2\geq2 ----> is true

therefore

Point C is a solution of the system of inequalities

Verify point D

F(3,4)

Inequality A


x\geq2 ----->
3\geq2 ----> is true

Inequality B


y\geq2 ------>
4\geq2 ----> is true

therefore

Point D is a solution of the system of inequalities

Part C: Natalie can only attend a school in her designated zone. Natalie's zone is defined by y < −2x + 2. Explain how you can identify the schools that Natalie is allowed to attend.

we have


y < -2x+2

The solution of the inequality is the shaded area below the dotted line
y=-2x+2

The y-intercept of the dotted line is the point (0,2)

The x-intercept of the dotted line is the point (1,0)

To graph the inequality, plot the intercepts and shade the area below the dotted line

see the attached figure N 2

therefore

The schools that Natalie is allowed to attend are A,B and D

The coordinate plane below represents a city. Points A through F are schools in the-example-1
The coordinate plane below represents a city. Points A through F are schools in the-example-2
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