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, often visualized as a shaded region on a graph.

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding linear equation as a boundary line. Then, use a dashed line for < or > and a solid line for ≤ or ≥. Finally, shade the appropriate region based on the inequality.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form of a linear equation is given by y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you determine if a point is part of the solution set for a linear inequality?

Back

To determine if a point is part of the solution set, 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 dashed line when 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 term 'boundary line' refer to in the context of linear inequalities?

Back

The boundary line is the line that represents the equation of the linear inequality. It divides the coordinate plane into two half-planes.

Front

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

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 identify the correct inequality from a graph?

Back

To identify the correct inequality from a graph, observe the slope and y-intercept of the boundary line, and determine whether the shaded region is above or below the line.

Front

What is a system of linear inequalities?

Back

A system of linear inequalities consists of two or more linear inequalities that are considered together, and the solution set is the region where all inequalities overlap.