4-4 Linear Inequalities

Front

What type of line is drawn when graphing a linear inequality with \( \leq \) or \( \geq \)?

Back

A solid line.

Front

What type of line is drawn when graphing a linear inequality with \( < \) or \( > \)?

Back

A dotted line.

Front

Which of the following represents a linear inequality: 'the number of students in the learning center is 20' or 'the number of students in the learning center is at most 20'?

Back

'The number of students in the learning center is at most 20' represents a linear inequality.

Front

Are the points on the line included in the solution set for inequalities with \( \leq \) or \( \geq \)?

Back

Yes, they are part of the solution set.

Front

What does the inequality \( y \leq \frac{2}{5}x + 1 \) represent graphically?

Back

It represents the region below and including the line \( y = \frac{2}{5}x + 1 \).

Front

How do you determine if a point is a solution to a linear inequality?

Back

Substitute the point's coordinates into the inequality and check if the statement is true.

Front

What is the general form of a linear inequality in two variables?

Back

It is typically written as \( ax + by < c \), \( ax + by \leq c \), \( ax + by > c \), or \( ax + by \geq c \).

Front

What does the term 'solution set' refer to in the context of linear inequalities?

Back

The solution set is the set of all points that satisfy the inequality.

Front

What is the significance of the boundary line in a linear inequality graph?

Back

The boundary line separates the solution set from the non-solution set.

Front

What does it mean if a linear inequality is graphed with a solid line?

Back

It means that points on the line are included in the solution set.