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 inequality 'y > -2' represent graphically?

Back

It represents all the points above the horizontal line y = -2, not including the line itself.

Front

How do you determine if a point is a solution to an 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.

Front

What does the inequality 'y ≥ 2x - 2' indicate?

Back

It indicates that the region includes the line y = 2x - 2 and all points above it.

Front

What is the difference between '>' and '≥' in inequalities?

Back

'>' means greater than and does not include the boundary line, while '≥' means greater than or equal to and includes the boundary line.

Front

What is a system of inequalities?

Back

A set of two or more inequalities with the same variables that are graphed on the same coordinate plane.

Front

How can you tell if a point is a solution to a system of inequalities?

Back

The point must satisfy all inequalities in the system simultaneously.

Front

What does the shaded region in a graph of an inequality represent?

Back

The shaded region represents all the possible solutions to the inequality.

Front

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

Back

The boundary line separates the solutions from the non-solutions; whether it is included or not depends on the type of inequality (>, <, ≥, ≤).

Front

How do you graph the inequality 'y < 2x + 3'?

Back

Graph the line y = 2x + 3 as a dashed line (not including the line) and shade below the line.