Graph Linear Inequalities In Two Variables

Front

What is a linear inequality in two variables?

Back

A linear inequality in two variables is an inequality that can be expressed in the form ax + by <, >, ≤, or ≥ c, where a, b, and c are constants and x and y are variables.

Front

What does the solution set of a linear inequality represent?

Back

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

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 part of the solution set.

Front

What is the difference between a solid line and a dotted line when graphing inequalities?

Back

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

Front

What does the symbol '>' indicate in a linear inequality?

Back

The symbol '>' indicates that the values of y are greater than the values of the expression on the right side of the inequality.

Front

What does the symbol '<' indicate in a linear inequality?

Back

The symbol '<' indicates that the values of y are less than the values of the expression on the right side of the inequality.

Front

How do you graph the inequality y > -x + 1?

Back

To graph y > -x + 1, first graph the line y = -x + 1 as a dotted line, then shade the region above the line.

Front

What is the significance of the inequality symbol in determining the type of line to draw?

Back

The inequality symbol determines whether to use a solid or dotted line: solid for ≤ or ≥, and dotted for < or >.

Front

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

Back

If a point lies above the line in a graph of an inequality, it means that the point satisfies the inequality.

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What does it mean if a point lies below the line in a graph of an inequality?

Back

If a point lies below the line in a graph of an inequality, it means that the point does not satisfy the inequality.