Graphing inequalities in 2 variables part1

Front

What is an inequality in two variables?

Back

An inequality in two variables is a mathematical statement that compares two expressions using inequality symbols (>, <, ≥, ≤) and involves two variables, typically x and y.

Front

What does the graph of an inequality represent?

Back

The graph of an inequality represents all the solutions that satisfy the inequality, showing the region of the coordinate plane where the inequality holds true.

Front

How do you graph the inequality y > 2x - 5?

Back

1. Graph the line y = 2x - 5 as a dashed line (since it's >, not ≥). 2. Shade the region above the line, indicating all points where y is greater than 2x - 5.

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 if a point is a solution to an 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 does the inequality y ≤ -3x + 4 represent graphically?

Back

It represents a region below or on the line y = -3x + 4, including the line itself, since the inequality is ≤.

Front

What is the solution set of the inequality x > -5?

Back

The solution set includes all real numbers greater than -5, represented graphically as a dashed line at x = -5 with shading to the right.

Front

How can you identify the correct graph for a given inequality?

Back

To identify the correct graph, analyze the inequality's slope and y-intercept, determine if the line is solid or dashed, and check which side of the line should be shaded.

Front

What does the inequality y < 1/2x + 2 indicate about the graph?

Back

It indicates that the region below the line y = 1/2x + 2 is included in the solution set, and the line itself is dashed.

Front

What is the significance of the slope in the inequality y ≥ mx + b?

Back

The slope (m) indicates the steepness and direction of the line, affecting how the inequality is graphed and which region is shaded.