Task #3: System of Linear Inequalities Graphs

Front

What is a linear inequality?

Back

A linear inequality is a mathematical statement that compares a linear expression to a value using inequality symbols (>, <, ≥, ≤).

Front

What does the solution of a linear inequality represent?

Back

The solution of a linear inequality represents all the points (x, y) that satisfy the inequality, often visualized as a region on a graph.

Tags

CCSS.HSA.REI.D.12

Front

How do you graph a linear inequality?

Back

1. Graph the corresponding linear equation as a solid line (for ≤ or ≥) or a dashed line (for < or >). 2. Shade the region that satisfies the inequality.

Tags

CCSS.HSA.REI.D.12

Front

What is the difference between a solid line and a dashed line in graphing inequalities?

Back

A solid line indicates that points on the line are included in the solution (≥ or ≤), while a dashed line indicates that points on the line are not included (> or <).

Tags

CCSS.HSA.REI.D.12

Front

What does the intersection of two inequalities represent?

Back

The intersection of two inequalities represents the set of points that satisfy both inequalities simultaneously.

Tags

CCSS.HSA.REI.D.12

Front

How can you determine if a point is a solution to a system of inequalities?

Back

Substitute the coordinates of the point into each inequality. If the point satisfies all inequalities, it is a solution.

Front

What is the graphical representation of the inequality y < 2x - 1?

Back

The graph will have a dashed line for y = 2x - 1, and the region below the line will be shaded.

Tags

CCSS.HSA.REI.D.12

Front

What does the inequality y ≥ -2x + 3 represent graphically?

Back

It represents a solid line for y = -2x + 3, with the region above the line shaded.

Tags

CCSS.HSA.REI.D.12

Front

What is a feasible region in the context of linear inequalities?

Back

A feasible region is the area on a graph where all constraints (inequalities) are satisfied, representing all possible solutions.

Tags

CCSS.HSA.REI.D.12

Front

How do you find the vertices of a feasible region?

Back

Vertices can be found by identifying the points of intersection of the boundary lines of the inequalities.

Tags

CCSS.HSA.REI.D.12