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# Precalculus MM: To the Docks (Jerome and Gate Guard): Linear Equations and Inequalities 1: NWN 0155b

Notes on graphing two variable inequalities:
1) Graph the line using y=mx+c techniques.
2) Dotted line > < or solid line >= or <=.
3) Shading: pick a test point, substitute the x and y values, shade the points that make the inequality true.
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An easy way for Zanzi to monitor the GP signal is by graphing its power to voltage ratio on an a coordinate grid projected internally onto her retina constructs. The graph is linear because power (y coordinate) and voltage (x coordinate) are proportional if the current is kept constant. Where the voltage is 0.800 V and 1.375 V, two solid vertical lines are plotted and the area between the two lines shaded. If points plotted on the power : voltage graph lie on either line or within the shaded region of 0.800 V <= voltage <= 1.375 V, then all is well.
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Notes on solving linear equations (in one variable):
The great relief Zanzi feels in sensing her Game Player is back on the Game system has put her in an elated mood; the last time she felt this content in the Game was just after she had levelled up to a level two bard, when she and Parvel were in Gelder's study in the Neverwinter Academy and she found books on how to solve linear equations where just one variable is involved. The trick is to isolate the variable on one side of the equation using the addition property of equality (or use of the additive inverse on both sides of the equation) to keep the equation balanced.
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Remembering this sparks memories of another time shortly after exiting Gelder's study when she and Parvel entered the dining room of the academy and she found a Potion of Bless, which has multiplicative properties to equally augment her attack and damage and Will saving throw against fear. This was where she learnt how to use the multiplication property of equality (or use of the multiplicative inverse on both sides of the equation) to isolate the variable in linear equations with one variable.
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The techniques for isolating the variable for linear equations in one variable are also used when solving for a parameter in a linear equation.