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 graph of a linear inequality represent?

Back

The graph of a linear inequality represents all the solutions (x, y) that satisfy the inequality. It is typically shown as a shaded region on one side of the boundary line.

Front

How do you graph the inequality y ≥ 7x - 3?

Back

1. Graph the line y = 7x - 3 as a solid line (since it includes equality). 2. Shade the region above the line to represent y values greater than or equal to the 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 (≥ or ≤), while a dashed line indicates that points on the line are not included (> or <).

Front

How do you determine the boundary line for the inequality y < -⅘(x) + 4?

Back

To determine the boundary line, graph the equation y = -⅘(x) + 4 as a dashed line, since the inequality is strict (<).

Front

What does the inequality y > -2x - 3 mean in terms of graphing?

Back

It means to graph the line y = -2x - 3 as a dashed line and shade the region above the line, indicating all points where y is greater than -2x - 3.

Front

What is the significance of the slope in a linear inequality?

Back

The slope indicates the steepness of the line and the direction in which the line rises or falls. It affects the region that is shaded in the graph.

Front

How do you solve a linear inequality like y ≤ (-3/4)x - 1?

Back

1. Graph the line y = (-3/4)x - 1 as a solid line. 2. Shade the region below the line to represent y values less than or equal to the line.

Front

What is the solution set of a linear inequality?

Back

The solution set of a linear inequality is the set of all ordered pairs (x, y) that satisfy the inequality, represented graphically by the shaded region.

Front

How can you check if a point is a solution to a linear inequality?

Back

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