How do you know when to shade above or below?

Unless you are graphing a vertical line the sign of the inequality will let you know which half-plane to shade. If the symbol ≥ or > is used, shade above the line. If the symbol ≤ or < is used shade below the line.

How do you use 0 0 as a test point?

Choose a point not on the line as a test point. The point (0,0) is an easy point to test, as long as it is not on the line. The test point will lie in one of the half-planes formed by the boundary line. If the test point makes the inequality true, shade that side of the line (shading over the point).

How do you graph inequalities and shade?

There are three steps:

  1. Rearrange the equation so “y” is on the left and everything else on the right.
  2. Plot the “y=” line (make it a solid line for y≤ or y≥, and a dashed line for y< or y>)
  3. Shade above the line for a “greater than” (y> or y≥) or below the line for a “less than” (y< or y≤).

Why is 0 0 A good choice for a test point?

Choose any convenient test point not on the boundary line. The origin (0, 0) is a good choice because it makes for easy calculation. Substitute x 0 and y 0 into the inequality.

What are the steps for solving inequalities?

To solve an inequality use the following steps:

  1. Step 1 Eliminate fractions by multiplying all terms by the least common denominator of all fractions.
  2. Step 2 Simplify by combining like terms on each side of the inequality.
  3. Step 3 Add or subtract quantities to obtain the unknown on one side and the numbers on the other.

How do you graph less than greater than?

How do you graph y less than 2?

Dashed lines tell the reader that the value is not included. So draw a parallel line to x -axis from y=2 point (0,2) . (The line should be dashed). And shade the area of the coordinate plane which y values are smaller than 2 .

Is the boundary line broken or solid?

solid line
The boundary line for the inequality is drawn as a solid line if the points on the line itself do satisfy the inequality, as in the cases of ≤ and ≥. It is drawn as a dashed line if the points on the line do not satisfy the inequality, as in the cases of < and >.

How do you find a solution to an inequality on a graph?


  1. Graph the first inequality. Graph the boundary line.
  2. On the same grid, graph the second inequality. Graph the boundary line.
  3. The solution is the region where the shading overlaps.
  4. Check by choosing a test point.
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