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 part of the solution set for 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 significance of the boundary line in a two-variable inequality?

Back

The boundary line represents the points where the inequality changes from true to false. If the inequality is strict (e.g., < or >), the line is dashed; if it is inclusive (e.g., ≤ or ≥), the line is solid.

Front

What does the inequality 'y < -4x - 1' represent graphically?

Back

A region below the line y = -4x - 1, where all points (x, y) satisfy the inequality.

Front

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

Back

Graph the line y = x + 2 as a solid line and shade the region above the line.

Front

What is the difference between 'y < mx + b' and 'y ≤ mx + b'?

Back

'y < mx + b' represents a region not including the boundary line, while 'y ≤ mx + b' includes the boundary line.

Front

What does the inequality '4y > -8' simplify to?

Back

y > -2.

Front

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

Back

By analyzing the slope and y-intercept of the inequality and determining the correct shading direction based on the inequality sign.

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.