Question 313034
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Step 1:  Determine the slope of the desired line.  In this case, you can simply do this by inspection.  That is because parallel lines have equal slopes and your given line is in slope-intercept form, namely: *[tex \Large y\ =\ mx\ +\ b]

Hence, the slope of the given line, which is the same as the slope we need for the desired line is just the coefficient on *[tex \Large x]

Step 2:  Use the point-slope form of the equation of a line to write an equation of the desired line:

*[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 slope of the desired line.  All you need do is plug in the numbers:

*[tex \LARGE \ \ \ \ \ \ \ \ \ \ y\ -\ (-1)\ =\ (-25)(x\ -\ (-1))]

Step 3:  The only thing left to do is to put this equation into slope-intercept form so that it matches the answer you gave.

Distribute across the parentheses in the RHS:

*[tex \LARGE \ \ \ \ \ \ \ \ \ \ y\ +\ 1\ =\ -25x\ -\ 25]

*[tex \LARGE \ \ \ \ \ \ \ \ \ \ y\ =\ -25x\ -\ 26]

Note that you cannot answer the question you asked exactly.  That is because you  wrote:  "Write <b><i>the</i></b> equation of the line that is parallel..."

The reason you can't do that is because there is no such thing as <b><i>the</i></b> equation of a line.  There are an infinite number of representations of any given line, so all you can do is to write <b><i>an</i></b> equation of the line you want.

Also, since you didn't specify the form of the answer, *[tex \LARGE  y\ =\ -25x\ -\ 26] is not the only valid answer to this question.  *[tex \LARGE  y\ +\ 1\ =\ (-25)(x\ +\ 1)] and *[tex \LARGE 25x\ +\ y\ =\ -26] are both equally valid answers to the question <i>as you posed it.</i>

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