Unit 5: Linear Inequalities STUDY GUIDE

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 such as <, >, ≤, or ≥.

Front

How do you graph a linear inequality?

Back

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

Front

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

Back

'≥' means 'greater than or equal to', indicating that the value can be either greater than or equal to the number.

Front

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

Back

'≤' means 'less than or equal to', indicating that the value can be either less than or equal to the number.

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 determine which side of the line to shade when graphing an inequality?

Back

Choose a test point not on the line (commonly (0,0)). Substitute it into the inequality. If the inequality holds true, shade the side containing the test point; otherwise, shade the opposite side.

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 by the shaded region on the graph.

Front

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

Back

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

Front

How do you convert a linear equation to slope-intercept form?

Back

To convert to slope-intercept form, solve for y in terms of x, isolating y on one side of the equation.

Front

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

Back

The y-intercept is the point where the line crosses the y-axis, representing the value of y when x = 0.