Graphing Systems of Linear Inequalities Warmup 3

Which system of inequalities matches the graph?

• y > 2x - 4
  y < 2

• y < 2x - 4
  y < 2

• y > 2x - 4
  y <  2 

• y < 2x - 4
  y <   -2

Answer explanation

The correct choice is y > 2x - 4 and y < 2, as the graph shows a region above the line y = 2x - 4 and below the line y = 2. The other options do not match the shaded area in the graph.

Tags

CCSS.HSA.REI.D.12

Consider the function y<2x+3. Which is true?

• The line would be solid with shading above.

• The line would be dashed with shading above.

• The line would be solid with shading below.

• None of these.

Answer explanation

The inequality y < 2x + 3 indicates a dashed line because it does not include equality. The shading is below the line, representing values less than the line. Therefore, the correct choice is 'None of these'.

Tags

CCSS.HSA.REI.D.12

Which of the following is a solution to the system of linear inequalities?

• (3,0)

• (0,0)

• (1,5)

• (2,2)

Answer explanation

The point (3,0) satisfies the system of linear inequalities, while the other points do not meet all the conditions set by the inequalities. Therefore, (3,0) is the correct solution.

Tags

CCSS.HSA.REI.D.12

Will my line be solid?
5 ≥ x

• Yes

• No

Answer explanation

The inequality 5 ≥ x means x can be any value less than or equal to 5. This creates a solid line on a graph, indicating all values up to and including 5 are valid. Therefore, the answer is Yes.

Which system of linear inequalities is represented by the graph?

• y≤2x-1
  y>-2x+3

• y>2x-1
  y≤-2x+3

• y<2x-1
  y≥-2x+3

• y≤2x-1
  y>2x+3

Answer explanation

The graph shows a line with a slope of 2, indicating y≤2x-1. The shaded area above the line y=-2x+3 suggests y>-2x+3. Thus, the correct system is y≤2x-1 and y>-2x+3.

Tags

CCSS.HSA.REI.D.12

Are the points on the line part of the solution set or not?

• Yes, they are part of the solution set

• No, they are NOT part of the solution set

Answer explanation

Yes, the points on the line are part of the solution set because they satisfy the equation represented by the line. Therefore, the correct answer is that they are part of the solution set.

Tags

CCSS.HSA.REI.D.12