Question 537833
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Parallel lines have equal slopes, so determine the slope of the given line by inspection since the equation is in slope-intercept form and then use the slope-intercept form to write an equation of the desired line.


Two things.  No line can have a *[tex \Large y]-intercept (or *[tex \Large x]-intercept for that matter) that is simply a number.  An intercept is a point and a point is described by an ordered pair (or triple or *[tex \Large n]-tuple depending on the number of dimensions you are in).  Hence it is incorrect to say that the *[tex \Large y]-intercept is 3.  Correctly stated, the *[tex \Large y]-intercept is *[tex \Large (0,3)]; the *[tex \Large y]-<b><i>coordinate</i></b> of the *[tex \Large y]-intercept is 3.


The slope-intercept form of an equation is *[tex \Large y\ =\ mx\ +\ b] where *[tex \Large m] is the slope and *[tex \Large b] is the *[tex \Large y]-coordinate of the *[tex \Large y]-intercept.  Just plug in the numbers and you are done. 


Second thing: Note that you cannot write "the" equation of any line.  You can only write "an" equation of a line.  In the first place, you could just substitute the values in the point-slope form and have an equation of the desired line, or you could solve for *[tex \Large y] to put it into slope-intercept form, or you could rearrange it into standard form, namely *[tex \Large Ax + By = C].  Furthermore, for a given *[tex \Large A], *[tex \Large B], and *[tex \Large C], *[tex \Large kAx + kBy = kC] where *[tex \Large k\ \in\ \mathbb{R}] describes a set of equations with an infinite number of elements, each of which graphs to the same line in *[tex \Large \mathbb{R}^2].


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