Graphing linear inequalities

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 (e.g., <, >, ≤, ≥).

Front

What does the symbol '≥' indicate in a linear inequality?

Back

The symbol '≥' indicates that the value on the left is greater than or equal to the value on the right.

Front

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

Back

Substitute the coordinates of the point into the inequality. If the inequality holds true, the point is a solution.

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 <).

Front

How can you tell if an inequality will have a dashed line?

Back

An inequality will have a dashed line if it uses the symbols '>' or '<', indicating that the boundary line is not included in the solution.

Front

What does the graph of a linear inequality represent?

Back

The graph of a linear inequality represents all the solutions that satisfy the inequality, typically shaded on one side of the boundary line.

Front

What is the first step in graphing a linear inequality?

Back

The first step is to graph the corresponding linear equation as if it were an equality.

Front

What does the term 'boundary line' refer to in graphing inequalities?

Back

The boundary line is the line that represents the equation of the inequality, separating the solution set from non-solution areas.

Front

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

Back

First, graph the line y = 2x + 1 with a dashed line, then shade below the line to represent y values less than 2x + 1.

Front

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

Back

The y-intercept is the point where the line crosses the y-axis, and it helps in graphing the inequality.