Linear Inequalities

Front

What type of line is used when graphing a linear inequality with \( \le \) or \( \ge \) signs?

Back

A solid line.

Front

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

Back

A dashed line.

Front

What does the inequality \( y > \frac{1}{2}x + 3 \) represent on a graph?

Back

The region above the line \( y = \frac{1}{2}x + 3 \).

Front

Which inequality represents the graph of a line with a slope of -\( \frac{4}{5} \) and a y-intercept of -1?

Back

\( y > -\frac{4}{5}x - 1 \) represents the area above the line.

Front

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

Back

Substitute the point's coordinates into the inequality; if the inequality holds true, the point is a solution.

Front

What is the graphical representation of the inequality \( y \ge 3x - 5 \)?

Back

The region above and including the line \( y = 3x - 5 \).

Front

What does the inequality \( y \le -\frac{1}{3}x - 5 \) indicate about the graph?

Back

It represents the area below and including the line \( y = -\frac{1}{3}x - 5 \).

Front

What is the significance of the y-intercept in a linear inequality?

Back

It indicates where the line crosses the y-axis, which helps in graphing the inequality.

Front

How do you graph the inequality \( y < 2x + 1 \)?

Back

Graph the line \( y = 2x + 1 \) as a dashed line and shade below it.

Front

What is the slope of the line represented by the inequality \( y \ge \frac{1}{3}x - 5 \)?

Back

The slope is \( \frac{1}{3} \).