Source: Manhattan Prep
Which of the following lines is perpendicular to 4x+5y=9 on the xy plane?
$$A.\ y=\frac{5}{4}x+2$$
$$B.\ y=\frac{-5}{4}x+9$$
$$C.\ y=-4x+\frac{9}{5}$$
$$D.\ y=\frac{4}{5}x+\frac{-4}{5}$$
$$E.\ y=\frac{-4}{5}x$$
The OA is A
Which of the following lines is perpendicular to 4x+5y=9
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- Jay@ManhattanReview
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Note that two lines are perpendicular to each other if the product of their slopes is 1.BTGmoderatorLU wrote:Source: Manhattan Prep
Which of the following lines is perpendicular to 4x+5y=9 on the xy plane?
$$A.\ y=\frac{5}{4}x+2$$
$$B.\ y=\frac{-5}{4}x+9$$
$$C.\ y=-4x+\frac{9}{5}$$
$$D.\ y=\frac{4}{5}x+\frac{-4}{5}$$
$$E.\ y=\frac{-4}{5}x$$
The OA is A
Let's first find out the slope of the given line 4x + 5y = 9. Let's transform it into y = mx + c form, where m is the slope of the line.
Thus, 4x+5y=9 => y = (-4/5)x + 9. Thus, m = -4/5
Say the slope of the line which is perpendicular to 4x+5y=9 is p.
Thus, mp = - 1. Thus, p = -1/m = -1/(-4/5) = 5/4.
The equation of the required line would be y = px + d, where p = slope of the line and d = y-intercept (We are not bothered about it).
The line presented by option A has a slope of 5/4, the correct answer.
The correct answer: A
Hope this helps!
-Jay
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- fskilnik@GMATH
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$$4x + 5y = 9\,\,\,\,\, \Leftrightarrow \,\,\,\,\,y = - {4 \over 5}x + {9 \over 5}\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{\rm{slope}} = - {4 \over 5}\,\,\,\,\,\,\left[ {{\rm{oblique}}\left( * \right)} \right]$$BTGmoderatorLU wrote:Source: Manhattan Prep
Which of the following lines is perpendicular to 4x+5y=9 on the xy plane?
$$A.\ y=\frac{5}{4}x+2 \,\,\,\,\,B.\ y=\frac{-5}{4}x+9\,\,\,\,\,C.\ y=-4x+\frac{9}{5}\,\,\,\,\,D.\ y=\frac{4}{5}x+\frac{-4}{5}\,\,\,\,\,E.\ y=\frac{-4}{5}x$$
$$?\,\,\,:\,\,\,\left( * \right)\,\,\, \Rightarrow \,\,\,{\rm{slop}}{{\rm{e}}_{{\rm{altern}}}} = {5 \over 4}\,\,\,$$
$$\left( {\rm{A}} \right)\,\,\,{\rm{slop}}{{\rm{e}}_{\left( {\rm{A}} \right)}} = {5 \over 4}\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{done}}!$$
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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We need to first express the given line in slope-intercept form, which is y = mx + b, where m is the slope of the line:BTGmoderatorLU wrote:Source: Manhattan Prep
Which of the following lines is perpendicular to 4x+5y=9 on the xy plane?
$$A.\ y=\frac{5}{4}x+2$$
$$B.\ y=\frac{-5}{4}x+9$$
$$C.\ y=-4x+\frac{9}{5}$$
$$D.\ y=\frac{4}{5}x+\frac{-4}{5}$$
$$E.\ y=\frac{-4}{5}x$$
The OA is A
5y = -4x + 9
y = (-4/5)x + 9/5
We see that the slope of the given line is -4/5. Since the slopes of two perpendicular lines are negative reciprocals of each other, then a line perpendicular to the given line will have a slope of 5/4. The line whose equation is given in choice A has that slope.
Answer: A
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