5.12 Graphing Linear Inequalities

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

What does the graph of a linear inequality represent?

Back

The graph of a linear inequality represents all the solutions that satisfy the inequality, typically shown as a shaded region on one side of a boundary line.

Front

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

Back

To determine if a point is a solution, substitute the coordinates of the point into the inequality. If the inequality holds true, the point is a solution.

Front

What is the difference between '>' and '≥' in linear inequalities?

Back

'>' means the boundary line is not included in the solution set (dashed line), while '≥' means the boundary line is included (solid line).

Front

What does the slope-intercept form of a linear equation look like?

Back

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

Front

How do you graph a linear inequality in two variables?

Back

1. Graph the boundary line (solid for ≥/≤, dashed for >/ <). 2. Choose a test point not on the line to determine which side to shade.

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, indicating the value of y when x=0.

Front

How can you convert a word problem into a linear inequality?

Back

Identify the quantities involved, determine the relationship (greater than, less than, etc.), and express it mathematically.

Front

What does the solution set of a linear inequality look like?

Back

The solution set is represented by the shaded region of the graph, indicating all possible solutions that satisfy the inequality.

Front

What is the role of the boundary line in graphing linear inequalities?

Back

The boundary line separates the solution set from the non-solution set and indicates whether points on the line are included or excluded.