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 Amsco Integrated Algebra I: Graphing First Degree Inequalities in Two Variables
This is a free lesson from our course in Amsco's Integrated Algebra
This lesson covers explanation of Graphing First Degree Inequalities in Two Variables and how to graph it. It’ll be done by the instructor in own hand writing by video presentation and with the help of several examples with solution. You may recall from earlier learning the basics of graphing in the coordinate plane, and that the expressions that utilize the relations <, ≤, > or ≥ are called inequalities. The solution set usually includes usually one or more intervals when graphed on a number line and graphing the solution set helps you visualize it.(More text below video...)
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(Continued from above) Graphing the linear inequalities involves the following steps:
• graph the equation that represents the boundary of the solution set (you may draw a solid line if the relation involves ≤ or ≥ and dashed line if it involves < or >.
• choose a point on the line and substitute its coordinates into the inequality.
• if the coordinates of the test point satisfy the inequality, shade the region that contains the point. In case test point coordinates don’t satisfy the inequality, shade the region on the other side of the line.

Remember: when the equation of a line is written in the form y = mx + b, the half-plane above the line is the graph of y > mx + b and the half-plane below the line is the graph of y < mx + b. Then check by shading the region of the half-plane where the selected point satisfies the inequality.
For Example: Graph the inequality y - 2x ≥ 2.To do it, you can proceed following the below given steps:
• transform the inequality into one having y as the left member i.e. y ≥ 2x + 2.
• graph the plane divider, y= 2x + 2, by using the y-intercept, 2, to locate the first point (0, 2) on the y-axis. Then use the slope, 2 to find other points by moving uj2 and to the right 1.
• shade the half-plane above the line.
• check the solution- choose any point in the half-plane selected as the solution to see whether it satisfies the original inequality, y - 2x ≥ 2. You’ll notice that the selected point (0, 5) which is in the shaded region satisfies it.

The video above explains more details on Graphing First Degree inequalities in two Variables, with the help of several examples and their solutions.

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