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 (>, <, ≥, ≤). It represents a region of the coordinate plane.

Front

How do you graph a linear inequality?

Back

1. Graph the corresponding linear equation as a dashed or solid line. 2. Use a dashed line for < or > (not including the line) and a solid line for ≤ or ≥ (including the line). 3. Shade the region that satisfies the inequality.

Front

What does the symbol '>' mean in a linear inequality?

Back

The symbol '>' means that the values of the variable are greater than the value on the other side of the inequality.

Front

What does the symbol '<' mean in a linear inequality?

Back

The symbol '<' means that the values of the variable are less than the value on the other side of the inequality.

Front

What does the symbol '≥' mean in a linear inequality?

Back

The symbol '≥' means that the values of the variable are greater than or equal to the value on the other side of the inequality.

Front

What does the symbol '≤' mean in a linear inequality?

Back

The symbol '≤' means that the values of the variable are less than or equal to the value on the other side of the inequality.

Front

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

Back

To determine if a point (x, y) is a solution, substitute the x and y values into the inequality. If the inequality holds true, then the point is a solution.

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

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