Systems of Inequalities

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

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

• A solid line is used for linear equations, while a dotted line is used for quadratic equations.

• A solid line represents a constant value, while a dotted line represents a variable value.

• A solid line indicates a positive slope, while a dotted line indicates a negative slope.

Which of the following inequalities matches the given graph? x ≥ -1, x ≤ -1, x > -1, x < -1

• x ≥ -1

• x ≤ -1

• x > -1

• x < -1

If the inequality symbol is > or ≥ you shade _________.

• below

• above

• to the left

• to the right

What is the purpose of graphing a system of inequalities?

• To visually represent the solution set where all inequalities overlap.

• To find the maximum value of a function.

• To determine the slope of a linear equation.

• To identify the roots of a polynomial.

What does it mean to shade below a line in a graph?

• It indicates that the solutions to the inequality are all the points below the line.

• It shows that the points above the line are not included in the solution.

• It represents the area where the function is increasing.

• It signifies that the line itself is part of the solution set.

If the inequality symbol is < or >, the line will be _________.

• dotted

• solid

• broken

• curved

What is the graphical representation of the inequality y < 2x + 3?

• The area above the line y = 2x + 3 is shaded.

• The area below the line y = 2x + 3 is shaded.

• The line y = 2x + 3 is dashed and the area above it is shaded.

• The line y = 2x + 3 is solid and the area below it is shaded.

What does the symbol ≥ mean in an inequality?

• It means 'less than or equal to'.

• It means 'greater than or equal to'.

• It means 'not equal to'.

• It means 'greater than'.

What is a system of inequalities?

• A single inequality with one variable.

• A set of two or more inequalities with the same variables.

• An equation that represents a straight line.

• A collection of unrelated inequalities.

What does the symbol ≤ mean in an inequality?

• It means 'greater than'.

• It means 'less than'.

• It means 'less than or equal to'.

• It means 'equal to'.