How do you graph linear inequalities in two variables?

Graphing linear inequalities in two variables is an important skill in mathematics, especially in algebra. It involves shading a region in a coordinate plane that satisfies the inequality, and then graphing the boundary line of the inequality.

To graph a linear inequality in two variables, you need to follow these steps:

1. First, graph the corresponding equation by plotting two points and drawing a straight line through them. Remember that the equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.
2. Next, choose a test point not on the line. This test point will determine which side of the line should be shaded. Substitute the x and y coordinates of the test point into the inequality. If the inequality is true, shade the side of the line that contains the test point. Otherwise, shade the other side of the line.
3. Finally, draw the boundary line of the inequality as a solid or dashed line, depending on whether the inequality includes or excludes the line, respectively. A solid line indicates that the boundary is included in the inequality, while a dashed line indicates that the boundary is excluded.

By following these steps, you can graph any linear inequality in two variables. Remember to label your axes and shade the appropriate region to make your graph clear and easy to read.