linear inequalities - graphing

Front

What is a linear inequality?

Back

A linear inequality is a mathematical statement that relates a linear expression to a value using inequality symbols (>, <, ≥, ≤) instead of an equal sign.

Front

What does the graph of a linear inequality represent?

Back

The graph of a linear inequality represents all the solutions that satisfy the inequality, typically shaded on one side of a boundary line.

Front

How do you determine if a line is solid or dashed when graphing a linear inequality?

Back

A solid line is used for inequalities that include equality (≥ or ≤), while a dashed line is used for strict inequalities (> or <).

Front

What does the inequality y < 3x - 4 represent graphically?

Back

It represents the region below the line y = 3x - 4, excluding the line itself.

Front

How do you graph the inequality y ≤ -3x + 1?

Back

Graph the line y = -3x + 1 as a solid line and shade below it to represent all points where y is less than or equal to -3x + 1.

Front

What is the solution set of the inequality y > -2?

Back

The solution set includes all points above the horizontal line y = -2.

Front

How do you test if a point is a solution to a linear inequality?

Back

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

Front

What does the inequality x ≥ 2 indicate about the shading on a graph?

Back

It indicates that the region to the right of the vertical line x = 2 should be shaded, including the line itself.

Front

What is the significance of the boundary line in graphing linear inequalities?

Back

The boundary line separates the solution set from the non-solution set and indicates whether points on the line are included (solid) or excluded (dashed).

Front

What type of line is represented by the inequality 5 ≥ x?

Back

It is represented by a solid vertical line at x = 5, shading to the left.