graphing inequalities on a coordinate plane

Shade the region that contains the ordered pairs that make the inequality a true statement. Identify at least one ordered pair on either side of the boundary line and substitute those `(x, y)` values into the inequality.Replace the `, =` sign in the inequality with ` = ` to find the equation of the boundary line. So how do you get from the algebraic form of an inequality, like `y>3x + 1`, to a graph of that inequality? Plotting inequalities is fairly straightforward if you follow a couple steps. Let’s take a look at one more example: the inequality `3x + 2yy`, sometimes making a table of values makes sense for more complicated inequalities. However, had the inequality been `x>=y` (read as ' `x` is greater than or equal to `y`'), then `(-2, -2)` would have been included (and the line would have been represented by a solid line, not a dashed line). It is not a solution as `-2` is not greater than `-2`. The ordered pair `(-2, -2)` is on the boundary line. In these ordered pairs, the `x`-coordinate is smaller than the `y`-coordinate, so they are not included in the set of solutions for the inequality. The ordered pairs `(-3, 3)` and `(2, 3)` are outside of the shaded area. These ordered pairs are in the solution set of the equation `x>y`. In these ordered pairs, the `x`-coordinate is larger than the `y`-coordinate. The ordered pairs `(4, 0)` and `(0, -3)` lie inside the shaded region. Is the `x`-coordinate greater than the `y`-coordinate? Does the ordered pair sit inside or outside of the shaded region? The graph below shows the region `x>y` as well as some ordered pairs on the coordinate plane. Let’s think about it for a moment-if `x>y`, then a graph of `x>y` will show all ordered pairs `(x, y)` for which the `x`-coordinate is greater than the `y`-coordinate. When the inequality symbol is replaced by an equal sign, the resulting related equation will graph as a straight line. Remember how all points on a line are solutions to the linear equation of the line? Well, all points in a region are solutions to the linear inequality A mathematical statement in two variables using the inequality symbols, ≤, or ≥ to show the relationship between two expressions. Next, the light red region that is to the right of the line (excluding the line `x = y)` represents the entire set of solutions for the inequality `x>y`.

First, the dashed red boundary line is the graph of the related linear equation `x = y`. There are a few things to understand here. The solution is a region, which is shaded. Here is what the inequality `x>y` looks like. One way to visualize two-variable inequalities is to plot them on a coordinate plane. Equations use the symbol `=` inequalities will be represented by the symbols ``, and `>=`. Inequalities and equations are both math statements that compare two values. Next, think of the first quadrant, (+,+), as someone wide-awake, or 'the active quadrant'.Linear inequalities are different than linear equations, although you can apply what you know about equations to help you understand inequalities.

You can then think of the third quadrant, (-,-), as someone sleeping, or 'the lazy quadrant'. You can think of the (+) as an open eye, (-) as a closed eye, and (,) as the mouth. You may have noticed that I put (-) to symbol a negative number an (+) to symbol a positive number. Eventually, this will become enrooted in your brain, and quizzes like this will be as easy as 123.Ģ) Look at the previous tip. You can then glance at your paper to see 'ok, in the third quadrant the number on the x-axis is positive and the number in the y-axis is negative. Finally, in the bottom left, write down (-,-). In the bottom right, write (+,-) then put a matching 4. In the upper left, write down '(-,+)' and mark it with a '2'. In the upper right corner, write (+,+) to symbol that both numbers are positive, then write '1'. Here's some tips to help you remember which quadrant is which:ġ) First off, draw down a coordinate plane. That's OK! This confusing topic definitely takes some practice before it feels natural.

Graphing inequalities on a coordinate plane