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 >).

Tags

CCSS.HSA.REI.D.12

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.

Tags

CCSS.HSA.REI.D.12

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 <).

Tags

CCSS.HSA.REI.D.12

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.

Tags

CCSS.HSA.REI.D.12

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.

Tags

CCSS.HSA.REI.D.12

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.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

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.

Tags

CCSS.8.EE.B.5

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.

Tags

CCSS.HSA.REI.D.12

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.

Tags

CCSS.HSA.REI.D.12