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

1. Graph the corresponding linear equation as a dashed or solid line. 2. Use a test point to determine which side of the line to shade.

Front

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

Back

The shaded region represents all the possible solutions to 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 they are not included (> or <).

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 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

What does 'rise over run' mean in the context of graphing?

Back

'Rise over run' refers to the slope of a line, calculated as the change in y (rise) divided by the change in x (run).

Front

How do you determine 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 is a system of inequalities?

Back

A system of inequalities consists of two or more inequalities that are considered simultaneously.

Front

How do you solve a system of inequalities by graphing?

Back

Graph each inequality on the same coordinate plane and identify the region where the shaded areas overlap.