IM Alg1.2.21 Lesson: Graphing Linear Inequalities in Two Variables (Part 1)
Here is an expression: . Decide if the values in each ordered pair, , make the value of the expression less than, greater than, or equal to 12.
Here are four inequalities:
- Find some coordinate pairs that represent solutions to the inequality and some coordinate pairs that do not represent solutions.
- Plot both sets of points. Either use two different colors or two different symbols like X and O.
- Plot enough points until you start to see the region that contains solutions and the region that contains non-solutions. Look for a pattern describing the region where solutions are plotted.
x≥y
-2y≥-4
3x<0
x+y>10
Here is a graph that represents solutions to the equation
Sketch 4 quick graphs representing the solutions to each of these inequalities using the applets below. Drag the red points to adjust the line, select a line style from the dropdown menu, and select on the blank areas on the graph to shade them in.
Sketch 4 quick graphs representing the solutions to each of these inequalities using the applets below. Drag the red points to adjust the line, select a line style from the dropdown menu, and select on the blank areas on the graph to shade them in.
x-y<5
x-y≤5
x-y>5
x-y≥5
For each graph, write an inequality whose solutions are represented by the shaded part of the graph.
The points and are both in the solution region of the inequality .
Compute for both of these points.
Which point comes closest to satisfying the equation ?
That is, for which pair is closest to 3?
The points and are also in the solution region. Which of these points comes closest to satisfying the equation ?
Find a point in the solution region that comes even closer to satisfying the equation . What is the value of ?
For the points and , . Find another point in the solution region for which .
Find for the point .Then find two other points that give the same answer.