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how is graphing a linear inequality similar to graphing a linear equation

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3 Answers

8x - 3y = 14
  Is an equation of a straight line, and shows graphically coordinates all point located on the line.
  8x - 3y > 4
  However shows the region of a plane away from the line in which
     8X -3y > 4    / the coordinates of the points where 8x -3y is greater than 4 , which is the part of the plane located in the left of the line.
Linear equations & linear inequalities are similar in that they are graphed as straight lines, with slope, y-intercepts, etc. As such, both can be understood, factored, and solved in the same ways. A major difference is that a linear equation has solutions that are on the line, while solutions of a linear inequality are not on the line. Often, a linear inequality indicates that the solution is "greater than" or "less than" the given expression, in which case the solution occupies part of a plane on one side of the line. When the expression indicates simply "not equal to," then the solution is both parts of the same plane except those points on the indicated line. It follows that "greater than or equal to" & "less than or equal to" will also include the points on the line as part of the solution. Linear equations, however, can have only those solutions represented by the points on the line.
In a linear inequality, such as the one you posted, all solutions will fall in the same plane & on the same side of the line.