Two Variable Inequalities

Front

What is a two-variable inequality?

Back

An inequality that involves two variables, typically written in the form of 'y < mx + b' or 'y ≥ mx + b', where m is the slope and b is the y-intercept.

Front

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

Back

The set of all points (x, y) that satisfy the inequality, often represented graphically as a shaded region on a coordinate plane.

Front

How do you determine if a point is a solution to a two-variable inequality?

Back

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 '>' and '≥' in inequalities?

Back

'>' means that the value is strictly greater than, while '≥' means that the value is greater than or equal to.

Front

What does the graph of 'y < 2x - 3' look like?

Back

A dashed line representing the equation y = 2x - 3, with the area below the line shaded to indicate all points where y is less than 2x - 3.

Front

What is the significance of a dashed line in graphing inequalities?

Back

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

Front

What does a solid line indicate in graphing inequalities?

Back

A solid line indicates that points on the line are included in the solution set (for '≥' or '≤' inequalities).

Front

How can you graph the inequality 'y ≥ -x + 1'?

Back

Graph the line y = -x + 1 with a solid line, then shade the area above the line to represent all points where y is greater than or equal to -x + 1.

Front

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

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you find the x-intercept of an inequality?

Back

Set y = 0 in the inequality and solve for x.