Question 999490
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When you are given two points, use the Two-Point form of an equation for a line.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ y\ -\ y_1\ =\ \left(\frac{y_1\ -\ y_2}{x_1\ -\ x_2}\right)(x\ -\ x_1) ]


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.


When you are given a slope and a point, use the Point-Slope form:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ y\ -\ y_1\ =\ m(x\ -\ x_1) ]


where *[tex \Large \left(x_1,y_1\right)] are the coordinates of the given point and *[tex \Large m] is the given or calculated slope.


If you are given an equation representing a line and asked to find an equation of a line parallel to that line through a given point, use:


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


and then use the Point-Slope form.


If you are given an equation representing a line and asked to find an equation of a line perpendicular to that line through a given point, use:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  L_1\ \perp\ L_2 \ \ \Leftrightarrow\ \ m_1\ =\ -\frac{1}{m_2}\ \text{ and } m_1,\, m_2\, \not=\, 0]


and then use the Point-Slope form.


If you are asked to put your answer in standard form, rearrange the equation to look like:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  Ax\ +\ By\ =\ C]


Some teachers/professors/instructors/textbook authors require that A, B, and C be integers, and some also require A to be a non-negative integer.


If you are asked to put your answer in Slope-Intercept form, rearrange the equation to look like:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \  y\ =\ mx\ +\ b]


where *[tex \Large m] is the slope of the line and *[tex \Large b] is the *[tex \Large y]-coordinate of the *[tex \Large y]-intercept.


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it

*[tex \Large \ \
*[tex \LARGE \ \ \ \ \ \ \ \ \ \