AnswersCMS 2026-2027 NC Math 1 CREDIT RECOVERYGraphing Two-Variable Linear Inequalities

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1
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Which is the graph of the linear inequality y is less than 3 x plus 1 ?

A
Image with description A coordinate plane displays the x-axis labeled from negative 5 to 5 in increments of 1 and the y-axis labeled from negative 5 to 5 in increments of 1. A solid line with a positive slope passes through approximately the points negative 1 comma negative 5, 0 comma 1, and 1 comma 5. The region to the left of the line is shaded.
B
Image with description A coordinate plane displays the x-axis labeled from negative 5 to 5 in increments of 1 and the y-axis labeled from negative 5 to 5 in increments of 1. A solid line with a positive slope passes through approximately the points negative 1 comma negative 5, 0 comma 1, and 1 comma 5. The region to the left of the line is shaded.
C
Image with description A coordinate plane displays the x-axis labeled from negative 5 to 5 in increments of 1 and the y-axis labeled from negative 5 to 5 in increments of 1. A solid line with a positive slope passes through approximately the points negative 1 comma negative 5, 0 comma 1, and 1 comma 5. The region to the left of the line is shaded.
D
Image with description A coordinate plane displays the x-axis labeled from negative 5 to 5 in increments of 1 and the y-axis labeled from negative 5 to 5 in increments of 1. A solid line with a positive slope passes through approximately the points negative 1 comma negative 5, 0 comma 1, and 1 comma 5. The region to the left of the line is shaded.
2
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Which is the graph of the linear inequality 1 half x minus 2 y is greater than negative 6 ?

A
Image with description A coordinate plane, both axis labeled from negative 10 to 10 with an increment of 2. A solid straight line has a positive slope and goes through negative 4 comma 2 and 4 comma 4. Everything above the line is shaded.
B
Image with description A coordinate plane, both axis labeled from negative 10 to 10 with an increment of 2. A solid straight line has a positive slope and goes through negative 4 comma 2 and 4 comma 4. Everything above the line is shaded.
C
Image with description A coordinate plane, both axis labeled from negative 10 to 10 with an increment of 2. A dashed straight line has a positive slope and goes through negative 4 comma 2 and 4 comma 4. Everything below the line is shaded.
D
Image with description A coordinate plane, both axis labeled from negative 10 to 10 with an increment of 2. A solid straight line has a positive slope and goes through negative 4 comma 2 and 4 comma 4. Everything above the line is shaded.
3

Which is the graph of the linear inequality 2 x minus 3 y is less than 12 ?

A
Image with description A coordinate plane has both the x and y axes labeled from negative 5 to 5. A dashed line is plotted with a positive slope that passes through the point 0 comma negative 4 and the point 3 comma negative 2. The region to the right of the line is shaded.
B
Image with description A coordinate plane has both the x and y axes labeled from negative 5 to 5. A solid line is plotted with a positive slope that passes through the point 0 comma negative 4 and the point 3 comma negative 2. The region to the right of the line is shaded.
C
Image with description A coordinate plane has both the x and y axes labeled from negative 5 to 5. A dashed line is plotted with a positive slope that passes through the point 0 comma negative 4 and the point 3 comma negative 2. The region to the left of the line is shaded.
D
Image with description A coordinate plane has both the x and y axes labeled from negative 5 to 5. A solid line is plotted with a positive slope that passes through the point 0 comma negative 4 and the point 3 comma negative 2. The region to the left of the line is shaded.
4

Which statements are true about the linear inequality y is greater than 3 fourths x minus 2 ? Choose three correct answers.

A
The area below the line is shaded.
B
The graph intersects the y -axis at 0 comma negative 2 .
C
The graph of y is greater than 3 fourths x minus 2 is a dashed line.
D
One solution to the inequality is 0 comma 0 .
E
The slope of the line is negative 2 .
5

Which is the graph of the linear inequality y is greater than or equal to negative x minus 3 ?

A
Image with description A coordinate plane with a dashed straight line with a negative slope. The x-axis is labeled from negative 5 to 5 in increments of 1 and the y-axis is labeled from negative 5 to 5 in increments of 1. The dashed line extends from the upper left, passing through approximately negative 2 comma 1 and continuing downward to the right toward approximately 1 comma negative 3, with the region below and to the right of the dashed line shaded, extending across the lower right portion of the coordinate plane.
B
Image with description A coordinate plane with a dashed straight line with a negative slope. The x-axis is labeled from negative 5 to 5 in increments of 1 and the y-axis is labeled from negative 5 to 5 in increments of 1. The dashed line extends from the upper left, passing through approximately negative 2 comma 1 and continuing downward to the right toward approximately 1 comma negative 4, with the region below and to the left of the dashed line shaded, extending across the lower left portion of the coordinate plane.
C
Image with description A coordinate plane with a straight line with a negative slope. The x-axis is labeled from negative 5 to 5 in increments of 1 and the y-axis is labeled from negative 5 to 5 in increments of 1. The line extends from the upper left, passing through approximately negative 2 comma 1 and continuing downward to the right toward approximately 1 comma negative 3, with the region below and to the right of the line shaded.
D
Image with description A coordinate plane with a straight line with a negative slope. The x-axis is labeled from negative 5 to 5 in increments of 1 and the y-axis is labeled from negative 5 to 5 in increments of 1. The line extends from the upper left, passing through approximately negative 2 comma 1 and continuing downward to the right toward approximately 1 comma negative 3, with the region below and to the right of the line shaded, extending across the lower right portion of the coordinate plane.
6

Which is the graph of the linear inequality 2 y is greater than x minus 2 ?

A
Image with description A coordinate plane with a dashed straight line with a positive slope. The x-axis and y-axis are labeled from negative 5 to 5 in increments of 1. The dashed line passes through the points negative 5 comma negative 4 and 4 comma 1, with the region below the line shaded.
B
Image with description A coordinate plane with a solid straight line with a positive slope. The x-axis and y-axis are labeled from negative 5 to 5 in increments of 1. The solid line passes through the points negative 1 comma negative 2 and 4 comma 1, with the region below the line shaded.
C
Image with description A coordinate plane with a dashed straight line with a positive slope. The x-axis and y-axis are labeled from negative 5 to 5 in increments of 1. The dashed line passes through the points negative 5 comma negative 4 and 4 comma 1, with the region above the line shaded.
D
Image with description A coordinate plane with a dashed straight line with a positive slope. The x-axis and y-axis are labeled from negative 5 to 5 in increments of 1. The dashed line passes through the points negative 5 comma negative 4 and 4 comma 1, with the region below the line shaded.
7

Which linear inequality is represented by the graph?

A
y is less than or equal to 1 half x plus 2
B
y is greater than or equal to 1 third x plus 2
C
y is greater than or equal to 1 half x plus 2
D
y is less than or equal to 1 third x plus 2
9

Which linear inequality is represented by the graph?

A
y is greater than or equal to 1 third x plus 4
B
y is less than or equal to 1 third x plus 4
C
y is less than or equal to 1 third x minus 4
D
y is greater than or equal to 1 third x minus 4
10

Which points are solutions to the linear inequality y is less than 0 point 5 x plus 2 ? Choose three correct answers.

A
negative 2 comma 1
B
negative 3 comma negative 2
C
negative 1 comma 2
D
1 comma negative 2
E
negative 1 comma negative 2

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