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 >).

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.

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

If the line is solid, use ≥ or ≤ in the inequality to include the boundary line in the solution.

Front

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

Back

If the line is dashed, use > or < in the inequality to exclude the boundary line from the solution.

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 the slope of a line represent in a linear inequality?

Back

The slope represents the rate of change of the dependent variable (y) with respect to the independent variable (x).

Front

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

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of y when x = 0.