Inequalities and Graph Interpretation Flashcard. 1st 12-4-24

Front

What does a dashed line indicate in a graph of an inequality?

Back

A dashed line indicates that the points on the line are not included in the solution set (i.e., the inequality is strict, such as < or >).

Front

What does a solid line indicate in a graph of an inequality?

Back

A solid line indicates that the points on the line are included in the solution set (i.e., the inequality is non-strict, such as ≤ or ≥).

Front

How do you solve the inequality 3x - 2 ≥ 34?

Back

Add 2 to both sides: 3x ≥ 36. Then divide by 3: x ≥ 12.

Front

Is (0,0) a solution to the inequality y > -x + 1?

Back

No, because substituting (0,0) gives 0 > 1, which is false.

Front

What is the correct graph for the inequality y > -2x - 3?

Back

The graph should be shaded above the line -2x - 3 with a dashed line.

Front

What does the inequality y < mx + b represent graphically?

Back

It represents the area below the line y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you determine if a point is a solution to an inequality?

Back

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

Front

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

Back

The y-intercept is the point where the line crosses the y-axis, which helps in graphing the inequality.

Front

What does the inequality x ≤ -12 mean in terms of graphing?

Back

It means that the solution set includes all points to the left of -12 on the x-axis, including -12 itself.

Front

How do you graph the inequality y ≥ 2x + 1?

Back

Graph the line y = 2x + 1 with a solid line and shade above the line.