Bunuel wrote:
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. \(y = \frac{-4}{5}x\)
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:
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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