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 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 do you find the slope of a line from a graph?

Back

The slope is found by calculating the rise over run, which is the change in y divided by the change in x 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 boundary line in a linear inequality?

Back

The boundary line separates the graph into two regions, one that satisfies the inequality and one that does not.

Tags

CCSS.HSA.REI.D.12

Front

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

Back

To determine if a point is a solution, substitute the x and y values of the point into the inequality. If the inequality holds true, the point is a solution.