Carcass wrote:
Which of the following is an equation of a line that is perpendicular to the line whose equation is 2x+ 3y= 4?
Indicate all such equations.
A) 3x+ 2y= 4
B) 3x— 2y = 4
C) 2x— 3y = 4
D) 4 — 3x= —2y
E) 4 + 2x = 3y
Two lines are perpendicular when the slope of one line is the negative reciprocal of the other.
If one line has a slope \(m\), then the other line must have a slope\(\frac{-1}{m}\)so that two lines are perpendicular.
Here the equation 2x+ 3y= 4
or we can re write in y= mx +b form
or 3y = -2x +4
or\(y= \frac{-2}{3} x +4\)
Here slope m = -2/3
Now the other line must have a slope of 3/2.
So looking at the equation option B
if we re write the equ in y = mx + b form we have
\(2y = 3x +4\)
or \(y = \frac{3}{2} x - 4\)
here slope m = 3/2
In equ D we re write the equ in y = mx + b form we have
\(2y = 3x + 4\)
or \(y = \frac{3}{2} x -4\).
Therefore option B and Option D are our possible answer
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