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 such as <, >, ≤, or ≥.

Front

What does the symbol '≥' mean in an inequality?

Back

The symbol '≥' means 'greater than or equal to'. It indicates that the value on the left is either greater than or equal to the value on the right.

Front

What does the symbol '≤' mean in an inequality?

Back

The symbol '≤' means 'less than or equal to'. It indicates that the value on the left is either less than or equal to the value on the right.

Front

How do you graph a linear inequality?

Back

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

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

Front

How do you convert a linear equation to a linear inequality?

Back

To convert a linear equation to a linear inequality, replace the equality sign '=' with an inequality symbol (<, >, ≤, or ≥) based on the context of the problem.

Front

What is the solution set of a linear inequality?

Back

The solution set of a linear inequality is the set of all points (x, y) that satisfy the inequality, represented graphically as a shaded region on the coordinate plane.

Front

What does it mean to solve a linear inequality?

Back

To solve a linear inequality means to find all values of the variable that make the inequality true, often resulting in a range of values.

Front

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

Back

To check if a point is a solution to a linear inequality, substitute the coordinates of the point into the inequality. If the inequality holds true, the point is a solution.

Front

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

Back

The slope-intercept form of a linear equation is given by the formula y = mx + b, where m is the slope and b is the y-intercept.