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 (e.g., <, >, ≤, ≥).

Front

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

Back

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

Front

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

Back

Substitute the x and y values 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 is y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope of a line represent?

Back

The slope represents the rate of change of y with respect to x; it indicates how steep the line is.

Front

What is the y-intercept of a line?

Back

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

Front

What type of line is used for inequalities with 'or equal to' symbols?

Back

A solid line is used for inequalities that include 'or equal to' (≥ or ≤).

Front

What type of line is used for strict inequalities?

Back

A dashed line is used for strict inequalities (greater than '>' or less than '<').

Front

How can you graph a linear inequality?

Back

1. Graph the corresponding linear equation as a line. 2. Use a solid or dashed line based on the inequality. 3. Shade the appropriate region based on the inequality.

Front

What does shading above the line indicate in a graph of an inequality?

Back

Shading above the line indicates that the solutions are greater than the line (y > mx + b).