Writing Linear Inequalities from 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 (>, <, ≥, ≤) instead of an equal sign.

Front

How do you represent a linear inequality graphically?

Back

A linear inequality is represented graphically by a shaded region on one side of a boundary line, which is either solid (for ≤ or ≥) or dashed (for < or >).

Front

What does the shaded area in a graph of a linear inequality indicate?

Back

The shaded area indicates all the possible solutions to the inequality, showing where the values satisfy the inequality.

Front

What is the difference between a solid line and a dashed line in the graph of a linear inequality?

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 do you write a linear inequality from a graph with a solid line?

Back

Identify the slope and y-intercept of the line, then write the inequality using ≥ or ≤, depending on the direction of the shading.

Front

How do you write a linear inequality from a graph with a dashed line?

Back

Identify the slope and y-intercept of the line, then write the inequality using > or <, depending on the direction of the shading.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

How can you determine the slope of a line from a graph?

Back

The slope can be determined by finding the rise over run between two points on the line.

Front

What does it mean if a linear inequality has no solution?

Back

A linear inequality has no solution if the shaded regions do not overlap, indicating that there are no values that satisfy the inequality.

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.