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

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Bunuel
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The line 3x + 4y = 8 passes through all of the quadrants in the coordi [#permalink] New post   10 May 2021, 21:00
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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.
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C
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Re: The line 3x + 4y = 8 passes through all of the quadrants in the coordi [#permalink] New post   11 May 2021, 09:57
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y = mx + c.

A line atmost passes through 3 quadrants.

Given line : 3x + 4y = 8

Standard form: \(y = \frac{-3}{4}x + 2\)

m = negative and c is positive. It will pass through 1,2 and 4 quadrants.

Case 1: m is positive and c is positive. The straight line will pass through 1,2 and 3 quadrants.

Case 2: m is negative and c is positive. The straight line will pass through 1,2 and 4 quadrants.

Case 3: m is positive and c is negative. The straight line will pass through 1,3 and 4 quadrants.

Case 4: m is negative and c is negative. The straight line will pass through 2,3 and 4 quadrants.

Answer C
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Re: The line 3x + 4y = 8 passes through all of the quadrants in the coordi [#permalink] New post   16 May 2021, 03:15
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Bunuel 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.

Answer: C.

Check the diagram below:


Hope it's clear.

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Re: The line 3x + 4y = 8 passes through all of the quadrants in the coordi [#permalink] New post   11 May 2021, 10:13
Asked: The line 3x + 4y = 8 passes through all of the quadrants in the coordinate plane except:
x/(8/3) + y/2 = 1
x-intercept = 8/3
y-intercept = 2

If we join the line with positive x-intercept and positive y-intercept, it will pass through I, II & IV quadrants.

IMO C
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Re: The line 3x + 4y = 8 passes through all of the quadrants in the coordi [#permalink] New post   16 May 2021, 03:21
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Solution:

Try the connect b/w slope and equation of the line

Also visualize the graph of such a line

3x + 4y = 8

=> Y = -(3/4)x + 2

=>Slope negative

=>The line passes through 1st,2nd and 4th quadrant and doesnt pass through 3rd(III) quadrant.

(option c)

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Re: The line 3x + 4y = 8 passes through all of the quadrants in the coordi [#permalink] New post   30 Jul 2023, 16:07
Hello from the GMAT Club BumpBot!

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Re: The line 3x + 4y = 8 passes through all of the quadrants in the coordi [#permalink]
30 Jul 2023, 16:07
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