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Graphing Linear Inequalities Worksheet with Answers
Here are the questions for Graphing Linear Inequalities Worksheet:
- On the grid, indicate the region clearly that satisfies all these Inequalities
x ≥ 3
y ≥ 1
x + y ≥ 5
- On the grid, indicate the region clearly that satisfies all these Inequalities
y < x
y ≥ 1
x + y ≤ 4
- On the grid, give label the region that satisfies all three of the following Inequalities
-1 < x < 2
y ≤ 8
y ≥ 4x – 4
- On the grid, give label the region which satisfies all three of the below Inequalities
x < 3
y > – 3
y > 2x
- On the grid, label the region clearly which satisfies all three of the below Inequalities
x ≤ 2
y < 2x -2
x + y + 2 > 0
- On the grid, label the region clearly which satisfies all three of the below Inequalities
x > 0
y ≥ ½ x
x + 2y < 4
- The greengrocer sells bananas and apples. In one day, he can sell up to 80 bananas, up to 90 apples, no more than a total of 110 pieces of fruit. Now, let x be the number of bananas sold. And, let y be the number of apples sold. Please show the region below that satisfies those Inequalities.
The region labeled R satisfies three Inequalities. Please state the three Inequalities.
The region labeled R satisfies three Inequalities. Please state the three Inequalities.
The region labeled R satisfies three Inequalities. Please state the three Inequalities.
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What are Linear Inequalities?
Talking about Graphing Linear Inequalities, now we are going to explain what Linear Inequalities are. Some of you may not know the definition about Linear Inequalities. Do not worry. Here we are going to explain about what Linear Inequalities are.
Linear inequalities look similar to slope intercept form equations, however use inequality operators instead of an equal sign. Here is an example Linear Inequality: y < 5x +2
Apparently, there are two additional steps that you need to take into account when graphing linear inequalities. The linear equality explains not only a line, but also whether values above or below the line are included in a set of possible solutions. This is usually shown by shading the area above or below the line to show that the shaded values are included.
Beyond shading, the line itself may not be included as part of the solution set. You are able to make this determination by looking at the inequality operator in linear inequality. If the inequality is less than or greater than in comparison, it means that the points which will fall on the line are not included in the solution itself. By convention, this is going to be shown in the graph of the linear equality by drawing a dashed line.
Once a linear inequality utilizes the greater than or less than or equal to inequality operators, it means that the points falling on the line are included in the solution set. In this case, a solid line is drawn on the coordinate plane to reflect it. With those two additional pieces of information, along with several previous skills in graphing linear equations, the steps to graph linear inequalities are easy enough.
How to Graph Linear Inequalities?
If you have a linear inequality in slope intercept form, you are able to use these steps below to graph that inequality on the coordinate plane:
Firstly, you have to identify the y-intercept constant in the inequality (the ‘b’ term in the equation). Please plot the y-intercept point on the coordinate plane at the (0,b) point. After that, you have to identify the slope constant in the inequality (the ‘m’ value). Then, convert it to a fraction over 1 or an improper fraction if it is not already in fraction form.
You have to treat the slope as a rise-over-run value. Then you are able to start at the y-intercept move along the y-axis. Please move along the x-axis a distance equal to the denominator of the slope. You are going to draw a line extending through the two plotted points, however the type of line depends on the inequality operator.
If the inequality is a simple ‘greater than’, or ‘less than,’ you are able to draw a dashed line to show the real values on the line are not included in the result. If the inequality is of the ‘or equal’ variety, you have to draw a solid line to show values on the line are included in the result. Also, you have to shade the area of the graph above or below the line based on the inequality operator.
For “greater than”, or “greater than or equal to” inequalities, you are able to shade y values which are above the line. For “less than”, or “less than or equal to” inequalities, you are able to shade y values which are below the line.
If you are graphing linear inequalities, the worksheets provide great practice resources for middle school algebra students. Also, you are able to print a blank coordinate field to graph other equations. Or you are able to try working with the slope calculator to view how different points are utilized to calculate slope and create an equation in point slope form.
