Step 2 : Determine which side of the line contains the solutions. Since y is less than the expression, you will shade belo w the line. 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.
Let's solve the first equation for y: Step 2: Substitute that equation into the other equation, and solve for x. When graphing a linear inequality on a number line, use an open circle for "less than " or " greater than ", and a closed circle for "less than or equal to " or " greater than or equal to ".
To graph a linear equation, we can use the slope and y-intercept. Locate the y-intercept on the graph and plot the point. From this point, use the slope to find a second point and plot it. Draw the line that connects the two points. Greater than and less than symbols can be used to compare numbers and expressions. This form of the equation of a line is called slope - intercept form.
The slope of a line, m, is a measure of its steepness. To solve an inequality sentence, use exactly the same procedure that you would if it were an equation, with the following exception.
When multiplying or dividing both sides of an inequality by a negative number, the direction of the inequality switches. The last step is to shade either above or below the boundary line. Evaluate the x and y values of the point into the inequality, and see if the statement is true. The variable y is found on the left side. In mathematics a linear inequality is an inequality which involves a linear function.
A linear inequality contains one of the symbols of inequality :. It shows the data which is not equal in graph form. Summary Many simple inequalities can be solved by adding, subtracting, multiplying or dividing both sides until you are left with the variable on its own. But these things will change direction of the inequality: Don't multiply or divide by a variable unless you know it is always positive or always negative.
If the test point makes the inequality true, shade that side of the line shading over the point. If the test point makes the inequality false, shade the other side of the line not shading over the point. Step 3: Shade the solution set. Choosing a test point on the line does not tell us which side of the line is the solution. We do not need a test point for that part. This line divides the xy- plane into two regions: a region that satisfies the inequality, and a region that does not.
Next, pick a point not on the line.
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