when graphing greater than, less than, etc. do you shade and if you do which way do I shade?
Graphing Linear Inequalities
1. Graph the boundary line. This is done by using an equal sign instead of
the inequality sign. The boundary line
is a dotted line if there's no equal sign in the inequality.
2. Shade the area that contains the solution. The solution is all points
above or below the boundary line. If
your inequality is y > 2x-4, the solution is above(>)the. If the inequality is y < 2x-4, the solution
is below(<) the line. Choose any point (x,y)in the shaded area and it will
satisfy your inequality. If you have a solid boundary line,y =< 2x-4, all
points on the boundary line should also satisfy the inequality.
I hope this will help.
Well, when it comes to graphing inequalities, you definitely don't want to throw shade at anyone (unless it's a shady graph). Instead, you shade certain regions to indicate the solution set.
For the "greater than" or "less than" inequalities, such as x > 3 or y < 2, you'll want to shade the region that's on the side of the inequality symbol where the values are greater or lesser. Imagine your shading hand has a magic marker, and you're coloring in the appropriate area.
Now, if you have an inequality like "greater than or equal to" or "less than or equal to," such as x ≥ 4 or y ≤ -1, you need to shade the entire region that satisfies the inequality, including the boundary line. So, be generous with your shading skills and cover both the line and the side it points towards.
Just remember: don't go overboard with the shading, or your graph might end up looking like a rainbow on steroids!
When graphing inequalities such as "greater than" or "less than," shading is used to indicate the solution region on a graph. The shading is done in a particular direction based on the type of inequality.
To determine which way to shade, follow these steps:
1. Identify the inequality sign in the given problem. For example, if the inequality is "x > 3," the sign is ">" (greater than).
2. Draw the boundary line on the graph based on the inequality. In this example, draw a vertical line at x = 3.
3. Choose a test point that is not on the boundary line. Substitute the values of the test point into the original inequality to determine if it satisfies the inequality.
4. If the test point satisfies the inequality, shade in the region containing the test point. Otherwise, shade in the opposite region.
5. If the inequality symbol includes an equal sign (≥ or ≤), the boundary line is part of the solution, so it should be drawn as a solid line. Otherwise, if the symbol is just > or <, the boundary line should be drawn as a dashed line because it is not included in the solution.
Remember, the direction of shading depends on the inequality sign. For a "greater than" symbol (>) or "greater than or equal to" symbol (≥), shade above the line. For a "less than" symbol (<) or "less than or equal to" symbol (≤), shade below the line.
When graphing inequalities such as "greater than," "less than," or "greater than or equal to/less than or equal to," you can represent the solution on a graph by shading a certain region.
To determine which region to shade, follow these steps:
1. Start by graphing the corresponding linear equation without the inequality symbol. For example, if the inequality is "x > 3," graph the equation "x = 3" (a vertical line passing through x = 3).
2. Identify the area that satisfies the inequality. This can be done by determining whether you need to shade the region above or below the graphed line, or to the left or right of it, depending on the inequality symbol.
a. If the inequality is "greater than" (>) or "greater than or equal to" (≥), shade the region above the line or to the right of it.
b. If the inequality is "less than" (<) or "less than or equal to" (≤), shade the region below the line or to the left of it.
3. In case of an absolute value inequality, such as "|x| < 2," you need to shade the region between two lines. First, graph the corresponding equation, which, in this example, is "x = 2" (a vertical line passing through x = 2). Next, graph another vertical line representing the negative value of the inequality, which is "-x = 2" (a vertical line passing through x = -2). Shade the region between these two vertical lines.
Remember to use a dashed line when the inequality involves "greater than" (>) or "less than" (<), and a solid line when it involves "greater than or equal to" (≥) or "less than or equal to" (≤). This distinction is crucial because a solid line indicates that the boundary itself is included in the solution, while a dashed line means the boundary is not included.
By following these steps, you will be able to accurately graph any inequality and shade the appropriate region on the graph.