This is a simple thing to check. The inequality will either be y< or y> (less than y or greater than y). You know the area above the x-axis, where y=0, is where y is greater and the area below is where y is less. So the area above your graphed line is where y is greater and the area below your line is where y is less. This is easiest to check in a linear portion of your graph, i.e. the minimum or maximum point on a parabola.
The first is 2-dimensional, the second is 1-dimensional.
Whereas the procedure for a linear equality is the same, the inequality defines all of the plane on one side (or the other) of the corresponding line.
In an inequality, you have to shade a side of a line to see show if the possible answers are greater than or equal to it
Graphing a linear equation in two variables results in a straight line, representing all the solutions that satisfy the equation, while graphing a linear inequality produces a region on one side of the line that includes all the solutions satisfying the inequality. The line itself is solid if the inequality is ≤ or ≥, indicating that points on the line are included, or dashed if the inequality is < or >, indicating that points on the line are not included. Additionally, the area shaded represents all the combinations of values that satisfy the inequality, contrasting with the single line for an equation.
When graphing a linear inequality, the first step is to replace the inequality symbol with an equal sign to graph the corresponding linear equation. This creates a boundary line, which can be solid (for ≤ or ≥) or dashed (for < or >) depending on whether the points on the line are included in the solution set. After graphing the line, you then determine which side of the line represents the solution set by testing a point (usually the origin if it's not on the line) to see if it satisfies the original inequality. Finally, shade the appropriate region to indicate the solutions to the inequality.
The first is 2-dimensional, the second is 1-dimensional.
Whereas the procedure for a linear equality is the same, the inequality defines all of the plane on one side (or the other) of the corresponding line.
In an inequality, you have to shade a side of a line to see show if the possible answers are greater than or equal to it
john
If it is <= or >=
Because the question is tautological. You are asking how something is the same as that very samne thing!
With the equal sign (=).
Hi
Graphing a linear equation in two variables results in a straight line, representing all the solutions that satisfy the equation, while graphing a linear inequality produces a region on one side of the line that includes all the solutions satisfying the inequality. The line itself is solid if the inequality is ≤ or ≥, indicating that points on the line are included, or dashed if the inequality is < or >, indicating that points on the line are not included. Additionally, the area shaded represents all the combinations of values that satisfy the inequality, contrasting with the single line for an equation.
When graphing a linear inequality, the first step is to replace the inequality symbol with an equal sign to graph the corresponding linear equation. This creates a boundary line, which can be solid (for ≤ or ≥) or dashed (for < or >) depending on whether the points on the line are included in the solution set. After graphing the line, you then determine which side of the line represents the solution set by testing a point (usually the origin if it's not on the line) to see if it satisfies the original inequality. Finally, shade the appropriate region to indicate the solutions to the inequality.
They are alike in that you graph the lines in the same way, but they are different because you have to shade in one side of the line
Linear programming is just graphing a bunch of linear inequalities. Remember that when you graph inequalities, you need to shade the "good" region - pick a point that is not on the line, put it in the inequality, and the it the point makes the inequality true (like 0