Two- Variable Inequalities

Front

What is a two-variable inequality?

Back

An inequality that involves two variables, typically written in the form of ax + by <, >, ≤, or ≥ c.

Front

What does the graph of a two-variable inequality represent?

Back

The graph represents all the solutions (ordered pairs) that satisfy the inequality.

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 set (≤ or ≥), while a dashed line indicates they are not included (< or >).

Front

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

Back

Substitute the coordinates of the point into the inequality. If the inequality holds true, the point is a solution.

Front

What is the solution set of the inequality y > 2x + 1?

Back

The solution set includes all points above the line y = 2x + 1, not including the line itself.

Front

How do you graph the inequality y ≤ -3/4x + 3?

Back

Graph the line y = -3/4x + 3 with a solid line, then shade below the line to represent all points where y is less than or equal to the line.

Front

What does the boundary line of an inequality represent?

Back

The boundary line represents the points where the inequality changes from true to false.

Front

What is the significance of the y-intercept in a two-variable inequality?

Back

The y-intercept is the point where the line crosses the y-axis, indicating the value of y when x = 0.

Front

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

Back

Analyze the slope and y-intercept of the inequality, then determine the direction of shading 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.