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Line l has the equation 2x + 3y – 2 = 0.
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Updated on: 17 Jan 2019, 05:15
Updated on: 17 Jan 2019, 05:15
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85% (00:47) correct
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Line L has the equation \(2x + 3y – 2 = 0.\)
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Quantity A |
Quantity B |
The slope of a line perpendicular to line L |
\(\frac{9}{7}\) |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Originally posted by CAMANISHPARMAR on 17 Jan 2019, 04:12.
Last edited by Carcass on 17 Jan 2019, 05:15, edited 1 time in total.
Last edited by Carcass on 17 Jan 2019, 05:15, edited 1 time in total.
Edited by Carcass
Re: Line l has the equation 2x + 3y – 2 = 0.
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17 Jan 2019, 05:23
17 Jan 2019, 05:23
1
CAMANISHPARMAR wrote:
Line L has the equation \(2x + 3y – 2 = 0.\)
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Quantity A |
Quantity B |
The slope of a line perpendicular to line L |
\(\frac{9}{7}\) |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Explanation::
The equation can be written as :
\(2x + 3y – 2 = 0.\)
or \(y = -(\frac{2}{3})x + 2\)
Here slope = \(-\frac{3}{2}\)
The slope to be perpendicular it should be negative reciprocal of the slop of line L
i.e = \(\frac{3}{2}\) = 1.5
QTYB = \(\frac{9}{7}\) = 1.2
Therefore QTY A < QTY B
Option A
Re: Line l has the equation 2x + 3y – 2 = 0.
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17 Jan 2019, 06:36
17 Jan 2019, 06:36
Expert Reply
CAMANISHPARMAR wrote:
Line L has the equation \(2x + 3y – 2 = 0.\)
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Quantity A |
Quantity B |
The slope of a line perpendicular to line L |
\(\frac{9}{7}\) |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
The equation given is linear and the quantity A talks of the slope, so let us convert that equation in slope form
The slope form of a line is \(y=mx+c\), so let us convert \(2x + 3y – 2 = 0\) in the slope form.
\(=>3y=2-2x........y=-\frac{2}{3}x+\frac{2}{3}\), thus slope = \(m = -\frac{2}{3}\)
If m is a slope of a line, the slope of a perpendicular line is \(\frac{-1}{m}\), therefore, A= -1/\(-\frac{2}{3}=\frac{3}{2}\)..
\(\frac{3}{2}\) is equal to \(\frac{3*3}{2*3}=\frac{9}{6}\), and \(\frac{9}{6}>\frac{9}{7}\)..
Thus A>B
A
