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 shaded on one side of the boundary line.

Front

What is the difference between a solid line and a dashed line in graphing inequalities?

Back

A solid line indicates that points on the line are included in the solution set (≥ or ≤), while a dashed line indicates that points on the line are not included (> or <).

Front

How do you determine the boundary line for a linear inequality?

Back

To determine the boundary line, convert the inequality to an equation (e.g., y = mx + b) and graph it.

Front

What does shading in the graph of a linear inequality indicate?

Back

Shading indicates the region of the graph that contains all the solutions to the inequality.

Front

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

Back

Substitute the coordinates of the point into the inequality. If the inequality holds true, the point is a solution.

Front

What is the y-intercept of the inequality y ≥ -3/4 x + 3?

Back

The y-intercept is the point where the line crosses the y-axis, which is (0, 3) for this inequality.

Front

What does the inequality x < -1 represent on a number line?

Back

It represents all numbers to the left of -1, not including -1 itself.

Front

If a point lies on a dashed boundary line, is it part of the solution set?

Back

No, points on a dashed boundary line are not included in the solution set.

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.