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 written in the form ax + by < c, ax + by > c, ax + by ≤ c, or ax + by ≥ c, where a, b, and c are constants.

Front

What does the shaded region represent in a graph of a linear inequality?

Back

The shaded region represents all the solutions to the inequality, indicating where the inequality holds true.

Front

What is the difference between a solid line and a dotted line in 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

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, then the point is a solution.

Front

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

Back

The symbol '>' means that the values of the expression on the left side of the inequality are greater than the value on the right side.

Front

What does the symbol '<=' mean in a linear inequality?

Back

The symbol '<=' means that the values of the expression on the left side of the inequality are less than or equal to the value on the right side.

Front

If the inequality is y < 2x + 3, what type of line is used to graph it?

Back

A dotted line is used to graph it because the inequality does not include equality.

Front

What is the solution set of the inequality y ≥ -x + 1?

Back

The solution set includes all points above and on the line y = -x + 1.

Front

How can you test if a point is in the solution set of an inequality?

Back

Substitute the point's coordinates into the inequality. If the resulting statement is true, the point is in the solution set.

Front

What is the significance of the y-intercept in the graph of a linear inequality?

Back

The y-intercept is the point where the line crosses the y-axis, and it helps in graphing the inequality.