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 (>, <, ≥, ≤).

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 that 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?

Back

To write a linear inequality from a graph, identify the slope and y-intercept of the boundary line, determine the direction of the inequality based on the shaded area, and use the appropriate inequality symbol.

Tags

CCSS.HSA.REI.D.12

Front

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

Back

The slope-intercept form is given by the equation 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 the y-intercept represent in a linear inequality?

Back

The y-intercept represents the point where the line crosses the y-axis, indicating the value of y when x is zero.

Tags

CCSS.HSA.REI.D.12

Front

What is the significance of the inequality symbol in a linear inequality?

Back

The inequality symbol indicates the relationship between the two expressions, showing whether one is greater than, less than, or equal to the other.

Front

How do you convert a linear equation to a linear inequality?

Back

To convert a linear equation to a linear inequality, replace the equality sign with an inequality symbol (>, <, ≥, ≤) based on the context.