Graphing linear inequalities

Front

What is a linear inequality?

Back

A linear inequality is a mathematical statement that compares a linear expression to a value using inequality symbols (>, <, ≥, ≤).

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding linear equation as a dashed line (for < or >) or a solid line (for ≤ or ≥). Then shade the region that satisfies the inequality.

Front

What does the shaded area represent in the graph of a linear inequality?

Back

The shaded area represents all the solutions to the inequality, indicating where the inequality holds true.

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 (≤ or ≥), while a dashed line indicates that points on the line are not included ( < or >).

Front

How can you determine if a point is a solution to a linear inequality?

Back

To determine if a point is a solution, substitute the point's coordinates into the inequality. If the inequality holds true, the point is a solution.

Front

What does it mean if a point lies on the boundary line of a linear inequality?

Back

If a point lies on the boundary line, it is a solution if the line is solid (≤ or ≥) but not a solution if the line is dashed (< or >).

Front

What is the standard form of a linear inequality?

Back

The standard form of a linear inequality is Ax + By < C, Ax + By > C, Ax + By ≤ C, or Ax + By ≥ C, where A, B, and C are constants.

Front

What is the slope-intercept form of a linear inequality?

Back

The slope-intercept form of a linear inequality is y < mx + b, y > mx + b, y ≤ mx + b, or y ≥ mx + b, where m is the slope and b is the y-intercept.

Front

How do you find the x-intercept of a linear inequality?

Back

To find the x-intercept, set y = 0 in the inequality and solve for x.

Front

How do you find the y-intercept of a linear inequality?

Back

To find the y-intercept, set x = 0 in the inequality and solve for y.