Question 184354
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You have three errors:


First, when you divided by -4 when deriving the slope-intercept form of the given equation, you should have had a result like this:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \ \ y = \frac{2}{4}x - 3 \ \ \Rightarrow\ \ y = \frac {1}{2}x - 3]


Rather than


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \ \ y = \frac{4}{2}x - 3 \ \ \Rightarrow\ \ y = 2x - 3]


Second you used the same slope number for your derived equation that you developed when you put your given equation in slope-intercept form.  What you developed was an equation for a line <i><b>parallel</b></i> to your incorrect slope-intercept version of the given equation rather than perpendicular to the given line.


You forgot the rule that perpendicular lines have slopes that are negative reciprocals of each other, or:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \ \ L_1 \perp L_2 \ \ \Leftrightarrow\ \ m_1 = \frac{-1}{m_2}]


In your case, *[tex \Large m_1 = \frac{2}{4} = \frac {1}{2}], therefore *[tex \Large m_2 = \frac{-1}{\frac{1}{2}} = -2]


And your derived equation should look like:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \ \ y - 4 = -2(x - 5) \ \ \Rightarrow\ \ y = -2x + 10 + 4 \ \ \Rightarrow\ \ y = -2x + 14]


Third, when you went from:


y - 4 = 4/2(x - 5)


to


y - 4 = 4/2x -20/5


You multiplied the -5 by 4 but then forgot to divide by 2.  Your result should have been


y - 4 = 4/2x - 10/5


Having said all of that, you really have the right idea about all of this.  You just made a couple of easy-to-make mistakes.  Keep up the good work.


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