Inequality which side to shade

If you are unsure of which side to shade, pick any point on the graph that's not on the line. You are choosing a test point to determine which side contains the solutions. I will choose 0,0 because this is the easiest point to substitute into the inequality to check for solutions.

Since 0,0 is a solution and is to the right of the line, ALL of the points to the right of the line are solutions! Therefore, we will lightly shade the area to the right of the line to show that this side of the line contains all of the solutions to the inequality.

Did you notice how our boundary line was a dotted line because of the less than symbol that was used in the inequality? Also, you may have realized that you shade below the dotted line because of the less than symbol in the inequality.

However, if you are unsure you can always choose a test point. I always use the point 0,0 if it's not on the line. Substitute 0,0 into the original inequality. If the math sentence is true once you substitute 0,0 , then that means that 0,0 is a solution and you shade the half plane that contains 0,0. If the math sentence is false when you substitute 0,0 , then that means that 0,0 is not a solution and the other half plane or the side of the line that does not contain 0,0 should be shaded.

For this second example, we'll need to rewrite the equation so that it's in slope intercept form before we graph. Also take note that the sign is greater than or equal to, so we will graph a solid line this time instead of a dotted line. This example will also demonstrate how to choose three solutions to the inequality.

Graph the following inequality. Then identify three solution to the inequality. Step 1 : We need to rewrite the inequality so that it is in slope intercept form. Step 2 : Graph the line.

Note that the line is solid because the inequality sign is greater than or equal to. Step 3 : Shade the solution set. Since y is greater than the expression, shade the side "above" the line. For more information, see How do I know which side to shade when graphing an inequality I found an answer from in. You will shade below the line, since it is For more information, see I have to graph this inequality ,but what side do I shade?

I found an answer from ca. For more information, see Systems of Linear Inequality Graph 10 points; due tomorrow This line divides the xy- plane into two I found an answer from www. For more information, see I need help with graphing linear inequalities.

Apr 29, If you can solve the inequality in such a way where you have a single variable by itself on one How do you write inequalities from graphs? For more information, see How do you know where to shade when graphing inequalities? Feb 26, He says that we should use a dotted line to plot an inequality which contains the symbols less than or greater than.

He also says that we should The graph is not always a solid line. For more information, see Algebra: Graphing Linear Inequalities. You can use a visual representation to figure out what values make the inequality true—and also which ones make it false. Linear Inequalities as Regions. Linear inequalities are different than linear equations, although you can apply what you know about equations to help you understand inequalities. Inequalities and equations are both math statements that compare two values.

One way to visualize two-variable inequalities is to plot them on a coordinate plane. The solution is a region, which is shaded. There are a few things to notice here.

Next, look at the light red region that is to the right of the line. Remember how all points on a line are solutions to the linear equation of the line? Well, all points in a region are solutions to the linear inequality representing that region. Look at each ordered pair. Is the x- coordinate greater than the y- coordinate? Does the ordered pair sit inside or outside of the shaded region? In these ordered pairs, the x- coordinate is larger than the y- coordinate.

In these ordered pairs, the x- coordinate is smaller than the y- coordinate, so they are not included in the set of solutions for the inequality. As you did with the previous example, you can substitute the x- and y- values in each of the x, y ordered pairs into the inequality to find solutions. Ordered Pair. Makes the inequality. If substituting x, y into the inequality yields a true statement, then the ordered pair is a solution to the inequality, and the point will be plotted within the shaded region or the point will be part of a solid boundary line.

A false statement means that the ordered pair is not a solution, and the point will graph outside the shaded region , or the point will be part of a dotted boundary line.