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# The line 3x + 4y = 8 passes through all of the quadrants in

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The line 3x + 4y = 8 passes through all of the quadrants in [#permalink]

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09 Oct 2012, 12:28
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The line 3x + 4y = 8 passes through all of the quadrants in the coordinate plane except:

A. I
B. II
C. III
D. IV
E. II and IV.
[Reveal] Spoiler: OA

Last edited by Bunuel on 09 Oct 2012, 13:56, edited 3 times in total.
Edited the question and added the OA.
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Re: The line 3x + 4y = 8 passes through all of the quadrants in [#permalink]

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09 Oct 2012, 14:21
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venmic wrote:
The line 3x + 4y = 8 passes through all of the quadrants in the coordinate plane except:

A. I
B. II
C. III
D. IV
E. II and IV.

Notice that if both x and y are negative, then both 3x and 4y will be negative. The sum of two negative values (3x and 4y) cannot give positive result (8). Thereore the line does not pass through the third quadrant, where both x and y are negative.

Check the diagram below:
Attachment:

graph.png [ 6.97 KiB | Viewed 5309 times ]
Hope it's clear.
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Re: The line 3x + 4y = 8 passes through all of the quadrants in [#permalink]

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09 Oct 2012, 16:14
venmic wrote:
The line 3x + 4y = 8 passes through all of the quadrants in the coordinate plane except:

A. I
B. II
C. III
D. IV
E. II and IV.

This is a line which doesn't pass through the origin. We know because there is a free term (which doesn't contain neither $$x,$$ nor $$y$$).
In this case, we can use the intercept form of the line equation: divide through the equation by the free term 8. We get:
$$\frac{3x}{8}+\frac{4y}{8}=1$$ or $$\frac{x}{8/3}+\frac{y}{8/2}=1$$, and finally $$\frac{x}{2\frac{2}{3}}+\frac{y}{2}=1$$.

Now, we can easily see that the $$x$$ intercept is $$2\frac{2}{3}$$ and the $$y$$ intercept is $$2.$$
So, our line passes through the points $$(2\frac{2}{3},0)$$ and $$(0,2)$$. Sketch the line through these two points.
It is a decreasing line which doesn't pass through the third quadrant.

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Re: The line 3x + 4y = 8 passes through all of the quadrants in [#permalink]

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25 Jan 2014, 04:54
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Re: The line 3x + 4y = 8 passes through all of the quadrants in [#permalink]

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21 May 2014, 06:50
Line : 3x + 4y = 8

Given line can be written as

x/(8/3) + y/(8/4) = 1

Comparing with the intercept form of the equation of line we get x axis intercept as 8/3 and y axis intercept as 8/4 = 2.

So this line cut an intercept of 8/3 on x axis and 2 on y axis.

Attachment:
File comment: intercept

gmat234.jpg [ 18.45 KiB | Viewed 3631 times ]

From fig.. Line does not pass through quadrant III. Hence answer is C
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The line 3x + 4y = 8 passes through all of the quadrants in [#permalink]

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22 Apr 2016, 04:34
The easiest method would be to find and x and y intercept of this line

To find x intercept put y = 0 in 3x+4y = 8 which will give x = 8/3
To find y intercept put x = 0 in 3x+4y = 8 which will give y = 2

Therefore we have 2 points on the line (8/3, 0) and (0, 2). The first point lies on +ve X-axis and second on +ve Y-axis.
You can quickly (and roughly) plot these 2 points to verify that a line joining these 2 points will pass through 1st, 2nd and 4th Quadrant. Hence it cannot pass through 3rd Quadrant.

The line 3x + 4y = 8 passes through all of the quadrants in   [#permalink] 22 Apr 2016, 04:34
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