GRAPHING INEQUALITIES - Emaths
GRAPHING INEQUALITIES
When you draw a straight line in a coordinate grid, it splits the grid into two halves, these being either side of the line. Each of these two halves represent inequalities. The line itself represents an equation.
For instance, lets consider the line [pic] Now lets draw the graph of [pic]
[pic]
We want the side where all the points have an
[pic]coordinate, which are [pic]
We shade the side that does NOT satisfy
this inequality.
In practice, it is extremely important that you read the question, as it is very subjective as to which side you may be asked to shade. Also, you need to check whether or not the inequality is of the type [pic] or [pic]
as you need to take this into account when you graph the line.
e.g. by shading in the UNWANTED side, show all the points that satisfy [pic]
As the inequality sign cannot equal 6, i.e. it is NOT [pic]then we must draw the line as a DASHED line.
• Start by drawing the line [pic];
• Take a point either side of it;
• One side of the line will represent [pic] and the other side [pic] you must decide which,
• Substitute into the original inequality the values of [pic]for each of the two points;
• Shade the side that does NOT represent (satisfy) the inequality.
[pic]
FINDING REGIONS
If you are given a set of inequalities to solve, you are being asked to find the region that satisfies the set in full. Ensure that you shade the UNWANTED sides for each inequality so as to avoid confusion from overlaps.
e.g. find the region that satisfies the following inequalities, label this with an R.
[pic]
• Draw each of the graphs, being
careful that [pic] is drawn with a dashed line;
• Take each line in turn;
• Take a point either side of it and decide which side satisfies the inequality for that particular graph;
• Where possible, take the Origin as one of the points. It is far easier to substitute in these values;
• Shade the UNWANTED side;
• Make sure that you do this for all the graphs. Do NOT assume which region is required.
DESCRIBING REGIONS
You may be required to write down a set of inequalities that satisfy a given region. You will,
• Either be given the equations of the lines from which each inequality has been produced;
• Be given most of the equations of the lines, but you have to find one of them first before using it;
• In the event of being asked to find an equation, this will probably be part of the question earlier on.
e.g. write down the inequalities which describe the shaded region.
❑ Check to see if the lines are bold or dashed;
❑ Ensure you know the equation of each line;
❑ As the question wants the shaded region, you need to eliminate the side of each line where this is not a part of the inequality;
❑ Write down each inequality, for each line, separately.
Solution Set: [pic]
-----------------------
This side of
the line is
[pic]
This side of
the line is
[pic][pic]
[pic]
Wanted Side
................
................
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