You probably have experience graphing lines in slope-intercept form (y = mx + b). When a line is in this form and has an = sign, it's a linear equation. If you switch the equals sign to an inequality (<,>,<,>) it becomes a linear inequality. For example, y = 2x - 8 is a linear equation, y > 2x - 8 is a linear inequality.
Linear inequalities can be written in other forms. For example, 2x + 3y < 12 is also a linear inequality. In this lesson, we'll mostly look at inequalities where the y is by itself on the left side.
The graphs of linear inequalities look a little different than the graphs of linear equations.
Graph with = Sign
When you graph a linear equation (with an = sign), the graph is just a straight line. All of the solutions to the equation all lie on the line. Let's look at an example: y = x + 3. This has a slope of 1 and a y-intercept of 3. Make sure to check out the lesson on graphing lines in slope-intercept form if you need a refresher.
The line above represents the solutions to the equation y = x + 3. You can pick any point on the line and write it down as a coordinate point. If you plug the x- and y-values into the equation, they should come out equal to each other. For example, the point (1,4) is on the line. If you plug in 1 for x and 4 for y, you get 4 = 1 + 3. Does 4 = 1 + 3? Yes, 4 = 4. The point (2,5) is also on the line. Does 5 = 2 + 3? Yes, this point is also a solution to the equation y = x + 3.
When you graph a linear equation (with an = sign), only the points ON the line are solutions.
Welcome to Kate's Math Lessons!
Teachers: make sure to check out the study guides and activities.