Graphing Linear Inequalities

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 standard form inequality to slope-intercept form?

Back

To convert from standard form Ax + By = C to slope-intercept form, solve for y: By = -Ax + C, then y = (-A/B)x + (C/B).

Front

What does the symbol '>' represent in an inequality?

Back

The symbol '>' means 'greater than'. It indicates that the value on the left is larger than the value on the right.

Front

What does the symbol '<' represent in an inequality?

Back

The symbol '<' means 'less than'. It indicates that the value on the left is smaller than the value on the right.

Front

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

Back

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

Front

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

Back

The symbol '≤' means 'less than or equal to'. It indicates that the value on the left is either smaller 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

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 graphical representation of a linear inequality?

Back

The graphical representation of a linear inequality is a shaded region on one side of the boundary line, which represents all the solutions to the inequality.

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 (≥ or ≤), while a dashed line indicates that points on the line are not included (> or <).

Front

How do you graph the inequality y > 2x + 2?

Back

1. Graph the line y = 2x + 2 with a dashed line. 2. Shade the region above the line to represent y values greater than 2x + 2.