Question 245911
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Slope formula:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ m\ =\ \frac{y_1\ -\ y_2}{x_1\ -\ x_2} ]


where *[tex \Large \left(x_1,y_1\right)] and *[tex \Large \left(x_2,y_2\right)] are the coordinates of the given points.


Parallel lines have equal slopes.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  L_1 \parallel L_2 \ \ \Leftrightarrow\ \ m_1 = m_2]


Perpendicular lines have slopes that are negative reciprocals of each other


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  L_1\ \perp\ L_2 \ \ \Leftrightarrow\ \ m_1\ =\ -\frac{1}{m_2} \text{ and } m_1,\, m_2\, \neq\, 0]


The distance formula is:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ d\ =\ sqrt{(x_1\ -\ x_2)^2\ +\ (y_1\ -\ y_2)^2}]


Graphing inequalities:


Change the inequality to an equation, then graph the line.  If the inequality includes equality (that is, it is less than or equal or greater than or equal) graph the line with a solid line.  If the inequality does not include equality (< or >), graph the line with a dashed line.  Select a point not on the line.  Substitute the coordinates of the selected point into the original inequality.  If the result is a true statement, shade in the side of the line that includes the test point.  If the result is false, shade in the other side.


For a system of inequalities, the solution set is the area where the shaded areas overlap.  If the boundary line is dashed, points on the line are not included.


By the way, the way you stated the inequality system question, it cannot be answered.  "The" point in the solution set does not exist -  there is an infinity of ordered pairs in the solution set.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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