Also, since y = 4 y = 4, the point is above the x x-axis. Since x = − 5 x = − 5, the point is to the left of the y y-axis.The first number of the coordinate pair is the xFigure 5.24). Plot the following points in the rectangular coordinate system and identify the quadrant in which the point is located: The graph of the inequality 2 y > 4 x – 6 is:Ī quick note about the problem above.\) Since ( − 3, 1) results in a true statement, the region that includes ( − 3, 1) should be shaded. Insert the x- and y-values into the inequalityĢ y > 4 x – 6 and see which ordered pair results in a true statement. The line is dotted because the sign in the inequality is >, not ≥ and therefore points on the line are not solutions to the inequality.įind an ordered pair on either side of the boundary line. You can use the x- and y- intercepts for this equation by substituting 0 in for x first and finding the value of y then substitute 0 in for y and find x.Ĭreate a table of values to find two points on the line, or graph it based on the slope-intercept method, the b value of the y-intercept is -3 and the slope is 2. To graph the boundary line, find at least two values that lie on the line x + 4 y = 4. O If points on the boundary line aren’t solutions, then use a dotted line for the boundary line. This will happen for ≤ or ≥ inequalities. O If points on the boundary line are solutions, then use a solid line for drawing the boundary line. Shade the region that contains the ordered pairs that make the inequality a true statement. O Identify at least one ordered pair on either side of the boundary line and substitute those ( x, y) values into the inequality. Replace the, ≤ or ≥ 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 > 3 x + 1, to a graph of that inequality? Plotting inequalities is fairly straightforward if you follow a couple steps. While you may have been able to do this in your head for the inequality x > y, sometimes making a table of values makes sense for more complicated inequalities. The boundary line is solid this time, because points on the boundary line 3 x + 2 y = 6 will make the inequality 3 x + 2 y ≤ 6 true.Īs you did with the previous example, you can substitute the x- and y-values in each of the ( x, y) ordered pairs into the inequality to find solutions. The graph below shows the region of values that makes this inequality true (shaded red), the boundary line 3 x + 2 y = 6, as well as a handful of ordered pairs. Let’s take a look at one more example: the inequality 3 x + 2 y ≤ 6. 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. 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 representing that region. This region (excluding the line x = y) represents the entire set of solutions for the inequality x > y. Next, look at the light red region that is to the right of the line. First, look at the dashed red boundary line: this is the graph of the related linear equation x = y. 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. Linear inequalities are different than linear equations, although you can apply what you know about equations to help you understand inequalities.
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