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13 Nov 2017, 13:57
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
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Question Stats:
78% (01:26) correct
22%
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wrong
based on 529
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Which of the following equations defines a line for which no points on the line lie in quadrant III?
A.\(y = –3x + 4\)
B.\(y = 3x + 4\)
C.\(y= \frac{X}{3}+4\)
D.\(y = –3x – 4\)
E. \(y = 3x – 4\)
A.\(y = –3x + 4\)
B.\(y = 3x + 4\)
C.\(y= \frac{X}{3}+4\)
D.\(y = –3x – 4\)
E. \(y = 3x – 4\)
13 Nov 2017, 18:05
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Gnpth
Conventional: find the intercepts and graph the line
Attachment:
lines.png [ 4.11 KiB | Viewed 20056 times ]
These equations are in point slope form, and the numbers aren't bad.
A. \(y = –3x + 4\)
\(x = 0: y = 4\)
\(y = 0: 3x = 4, x = \frac{4}{3}\)
POINTS \((0,4) , (\frac{4}{3}, 0)\)
B. \(y = 3x + 4\)
\(x = 0: y = 4\)
\(y = 0: -3x = 4, x = -\frac{3}{4}\)
POINTS \((0, 4) and (-\frac{3}{4}, 0)\)
C. \(y= \frac{X}{3}+4\)
\(x = 0: y = 4\)
\(y = 0: \frac{x}{3} = -4, x = -12\)
POINTS \((0, 4) and (-12, 0)\)
D. \(y = –3x – 4\)
\(x = 0: y = -4\)
\(y = 0: 3x = -4, x = -\frac{4}{3}\)
POINTS (\(0, -4) and ( -\frac{4}{3}, 0)\)
E. \(y = 3x – 4\)
\(x = 0: y = -4\)
\(y = 0: 3x = 4, x = \frac{4}{3}\)
POINTS \((0, -4) and (\frac{4}{3}, 0)\)
See diagram. Only A avoids Q III.
ANSWER A
Sketch generally: watch slope and y-intercept
This way is a lot faster: Figure out whether the line's slope and y-intercept should be positive or negative.
Sketch the two absolute cases: a line with a positive slope through the origin, and one with a negative slope through the origin. Go from there.
Attachment:
lines2.png [ 16.48 KiB | Viewed 19615 times ]
Reject this one. We need to avoid Quadrant III. We need a negative slope
2) Sketch a line with a negative slope that passes through the origin
Lines with negative slopes always pass through Quadrants II and IV. How to avoid Q III?
3) Shift the line with the negative slope from the origin so that it does not pass through Q III
Note the y-intercept: it is positive
4) We need: a line with NEGATIVE slope and POSITIVE y-intercept
Check the options: Answers, B, C, and E are eliminated. Their slopes are positive
A. \(y = –3x + 4\)
Slope is -3
y-intercept is 4 (if x = 0, y = 4) KEEP
D. \(y = –3x – 4\)
Slope is -3
y-intercept is -4 (if x = 0, y = -4) REJECT
ANSWER A
General Discussion
13 Nov 2017, 16:02
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Gnpth
The question simply asks line that does not have either x or y with NEGATIVE sign
A.\(y = –3x + 4\).......If x is negative then y is always positive............Keep....There is no points on the line lie in quadrant III.
B.\(y = 3x + 4\)........x = -2, then y = -2.........................................Eliminate
C.\(y= \frac{X}{3}+4\)........x = -36, then y = - 9.......... .Eliminate
D.\(y = –3x – 4\)................................x = -1 , then y = -1.............Eliminate
E. \(y = 3x – 4\).................................x = -1 , then y = -7.............Eliminate
Answer: A
