Graphing Linear Equations and Inequalities

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the change in y (rise) over the change in x (run).

Front

How do you calculate the slope between two points (x1, y1) and (x2, y2)?

Back

Slope (m) = (y2 - y1) / (x2 - x1).

Front

What does a positive slope indicate about a line?

Back

A positive slope indicates that as x increases, y also increases, resulting in an upward slant from left to right.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as x increases, y decreases, resulting in a downward slant from left to right.

Front

What does a slope of zero mean?

Back

A slope of zero means the line is horizontal, indicating that y does not change as x changes.

Front

What does an undefined slope mean?

Back

An undefined slope occurs in vertical lines where x does not change, leading to division by zero in the slope formula.

Front

What is the difference between a linear equation and a linear inequality?

Back

A linear equation represents a straight line, while a linear inequality represents a region of the coordinate plane that satisfies the inequality.

Front

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

Back

The symbol '≥' indicates that the values are greater than or equal to a certain number.

Front

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

Back

The symbol '≤' indicates that the values are less than or equal to a certain number.

Front

How can you tell if a line is solid or dashed in graphing inequalities?

Back

A solid line indicates 'or equal to' (≥ or ≤), while a dashed line indicates 'greater than' (>) or 'less than' (<).