Two-Variable Inequalities

Front

What is a two-variable inequality?

Back

A two-variable inequality is a mathematical statement that compares two expressions involving two variables, typically written in the form of 'ax + by < c', 'ax + by > c', 'ax + by ≤ c', or 'ax + by ≥ c'.

Front

What does the solution set of a two-variable inequality represent?

Back

The solution set of a two-variable inequality represents all the ordered pairs (x, y) that satisfy the inequality, often visualized as a shaded region on a graph.

Front

How do you determine if a point is in the solution set of a two-variable inequality?

Back

To determine if a point (x, y) is in the solution set, substitute the x and y values into the inequality. If the inequality holds true, the point is part of the solution set.

Front

What is the significance of the boundary line in a two-variable inequality?

Back

The boundary line represents the points where the inequality becomes an equation. If the inequality is strict (< or >), the line is dashed; if it is inclusive (≤ or ≥), the line is solid.

Front

What does the graph of 'y < -4x - 1' look like?

Back

The graph of 'y < -4x - 1' is a dashed line with a slope of -4 and a y-intercept of -1, with the area below the line shaded.

Front

How do you graph the inequality '4y > -8'?

Back

To graph '4y > -8', first rewrite it as 'y > -2'. Then, draw a dashed horizontal line at y = -2 and shade the area above the line.

Front

What is the difference between '4y < -2' and '4y > -2'?

Back

'4y < -2' represents the area below the line y = -0.5, while '4y > -2' represents the area above the same line.

Front

What does the inequality '4y - 3x > 20' represent graphically?

Back

The inequality '4y - 3x > 20' represents a region above the line 4y = 3x + 20, which is a solid line if the inequality is inclusive.

Front

What is the role of test points in graphing inequalities?

Back

Test points are used to determine which side of the boundary line to shade. By substituting a test point into the inequality, you can see if the point satisfies the inequality.

Front

What is a dashed line in the context of inequalities?

Back

A dashed line indicates that the points on the line are not included in the solution set for strict inequalities (< or >).