02/04/2022 - Graphing Linear Inequalities

Front

What is a linear inequality?

Back

A linear inequality is a mathematical statement that relates a linear expression to a value using inequality symbols (e.g., <, >, ≤, ≥).

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding linear equation as a dashed or solid line, then shade the appropriate region based on the inequality symbol.

Front

What does the symbol '≥' indicate in an inequality?

Back

The symbol '≥' indicates that the value on the left is greater than or equal to the value on the right.

Front

What is the y-intercept of a linear equation?

Back

The y-intercept is the point where the graph of the equation crosses the y-axis, represented as (0, b) in the equation y = mx + b.

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

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

What does the solution set of a linear inequality represent?

Back

The solution set represents all the points (x, y) that satisfy the inequality, often visualized as a shaded region on a graph.

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How can you find the slope of a line from its equation?

Back

In the slope-intercept form y = mx + b, 'm' represents the slope of the line.

Front

What is the slope of the line represented by the equation y = -3/2x + 3?

Back

The slope of the line is -3/2.

Front

What does it mean if a point lies above the line in a graph of a linear inequality?

Back

If a point lies above the line, it means that the point satisfies the inequality if the inequality is of the form y > mx + b or y ≥ mx + b.