graphing inequalities on a coordinate plane

So you should shade the half‐plane that does not contain (1, 1) as shown in Figure 4. Two or more linear inequalities grouped together form a system of linear inequalities. If in doubt, or to check, plug in a pair of coordinates. Since y ≥ 2 x, you should shade the upper half‐plane. Graph y = 2 x to find the boundary (use a solid line, because the inequality is “≥”) as shown in Figure 3.įigure 3. Now dividing each side by –1 (and changing the direction of the inequality) gives A closed half‐plane includes the boundary line and is graphed using a solid line and shading.įirst transform the inequality so that y is the left member. If the inequality is a “≤”or “≥”, then the graph will be a closed half‐plane. This checking method is often simply used as the method to decide which half‐plane to shade.

You should shade the side that does not contain the point (0, 0). Since the point (0, 0) does not make this inequality a true statement, If the coordinates you selected do not make the inequality a true statement, then shade the half‐plane not containing those coordinates. If the coordinates you selected make the inequality a true statement when plugged in, then you should shade the half‐plane containing those coordinates. To check to see whether you've shaded the correct half‐plane, plug in a pair of coordinates-the pair of (0, 0) is often a good choice. Now shade the lower half‐plane as shown in Figure 2, since y < x – 3. An open half‐plane does not include the boundary line, so the boundary line is written as a dashed line on the graph.įirst graph the line y = x – 3 to find the boundary line (use a dashed line, since the inequality is “<”) as shown in Figure 1.įigure 1. If the inequality is a “>” or “<”, then the graph will be an open half‐plane. Before graphing a linear inequality, you must first find or use the equation of the line to make a boundary line. The graph of a linear inequality is always a half‐plane. This line is called the boundary line (or bounding line). Quiz: Linear Inequalities and Half-PlanesĮach line plotted on a coordinate graph divides the graph (or plane) into two half‐planes.Solving Equations Containing Absolute Value.Inequalities Graphing and Absolute Value.Quiz: Operations with Algebraic Fractions.Quiz: Solving Systems of Equations (Simultaneous Equations).Solving Systems of Equations (Simultaneous Equations).Quiz: Variables and Algebraic Expressions.Quiz: Simplifying Fractions and Complex Fractions.

Simplifying Fractions and Complex Fractions.

Quiz: Signed Numbers (Positive Numbers and Negative Numbers).

Signed Numbers (Positive Numbers and Negative Numbers).

Quiz: Multiplying and Dividing Using Zero.

Quiz: Properties of Basic Mathematical Operations.

Properties of Basic Mathematical Operations.

Therefore, this area is the area where the inequality holds true.

The area (region) to the right side of this has all the points with x < 1. We know that line $x=1$ is a vertical line passing through $x=1$. We can shade that area by drawing the line $x=1$ as this line makes the boundary condition for the inequality. It will be an area where all the points have x < 1. Now, if we plot the above inequality then we have to consider all the points on the coordinate plane where the x-coordinate is greater than one. Here, the length (L) of the stick is unknown but it is true that the length is less than one metre. Now, we approximate the length of the stick and we surely know that the stick cannot be more than one metre (by using some other stick whose length is exactly one metre). However, we do not have any measuring instrument to measure its length. In other words, we can say that the value of the quantity is not exactly known but we do know some restriction or condition for the value of the quantity.įor example, suppose we have a stick in our hand and we want to measure the length of that stick. Let us first understand what is meant by an inequality.Īs the same suggests, inequality refers to something (say some variable) being not exactly equal to something. First, plot the line for the equation $x=1$ and then shade the area for which the x coordinates of all the points in that area are less than 1. Hint: The plot of an inequality is an area on a coordinate plane.

Graphing inequalities on a coordinate plane