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 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 do you graph a linear inequality in two variables?

Back

1. Graph the corresponding linear equation as a boundary line. 2. Use a dashed line for '<' or '>' and a solid line for '≤' or '≥'. 3. Shade the region that satisfies the inequality.

Front

What does the inequality y < 2x + 3 represent graphically?

Back

It represents the area below the line y = 2x + 3, with a dashed line indicating that points on the line are not included.

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 linear inequality into slope-intercept form?

Back

To convert, isolate y on one side of the inequality. For example, from 3x - 2y < 10, rearrange to get y > (3/2)x - 5.

Front

What does the inequality y ≥ -x + 4 indicate about the graph?

Back

It indicates that the region above and including the line y = -x + 4 is part of the solution set.