Linear Inequalities

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 (>, <, ≥, ≤).

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 solution set of a linear inequality represent?

Back

The solution set of a linear inequality represents all the points (x, y) 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 (≤ or ≥), while a dashed line indicates that points on the line are not included ( < or >).

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.

Front

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

Back

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

Front

What is the 'rise over run' method in graphing?

Back

The 'rise over run' method involves using the slope (m) of the line to determine how much to rise (change in y) and how much to run (change in x) from one point to another.

Front

What is a system of inequalities?

Back

A system of inequalities is a set of two or more inequalities with the same variables. The solution is the region where the shaded areas of all inequalities overlap.

Front

How do you determine if a point is a solution to a system of inequalities?

Back

To determine if a point is a solution, substitute the point's coordinates into each inequality. If the point satisfies all inequalities, it is a solution.

Front

What does it mean for a point to be a solution to a linear inequality?

Back

A point is a solution to a linear inequality if it makes the inequality true when the coordinates are substituted into the inequality.