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 (>, <, ≥, ≤) instead of an equal sign.

Front

What does the symbol '≥' indicate in a linear 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 line is solid or dotted in graphing linear inequalities?

Back

A solid line is used when the inequality includes 'or equal to' (≥ or ≤), while a dotted line is used when it does not (> or <).

Front

What does shading above the line in a graph of a linear inequality represent?

Back

Shading above the line represents that the solutions to the inequality are greater than the line's equation.

Front

What does shading below the line in a graph of a linear inequality represent?

Back

Shading below the line represents that the solutions to the inequality are less than the line's equation.

Front

How can you tell 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, then 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 in a graph?

Back

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

Front

How do you graph a linear inequality?

Back

First, graph the corresponding linear equation as a solid or dotted line, then shade the appropriate region based on the inequality.

Front

What is the difference between 'y < mx + b' and 'y ≤ mx + b'?

Back

'y < mx + b' uses a dotted line and shades below, while 'y ≤ mx + b' uses a solid line and shades below.