In the xy-plane, if line k has negative slope and passes through the point (-5,r), is the x intercept of line k positive?
1. the slope of line k is -5
2. r > 0
Please support your answers with explanations. Thanks!
xy plane
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- logitech
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y = mx+b , where m is the slopebeater wrote:In the xy-plane, if line k has negative slope and passes through the point (-5,r), is the x intercept of line k positive?
1. the slope of line k is -5
2. r > 0
Please support your answers with explanations. Thanks!
X intercept of the line is at (X,0) so :
0 = mx+b
x= -b/m
so we will try to find out whether -b/m is positive or not.
1) m=-5 no info given for b
r = (-5)(-5)+b
r = 25+b
b=r-25 We dont know what r is so we can not decided whethjer -b/m is postive = 25-r/-5
2) r > 0
r = -5m+b
-5m+b > 0
b > 5m
5m is a negative value since We know that slope is NEGATIVE
so we can not decide whether b is positive or negative
INSUF
Statement 1 & 2
r = 25+b
25+b > 0
b > -25
It could be Postie or Negative
So I would go with E
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In the xy-plane, if line k has negative slope and passes through the point (-5,r), is the x intercept of line k positive?
1. the slope of line k is -5
2. r > 0
equation of a line
Y = MX + C
given that m = -ve
r = -5m + c
c = r+5m
x intercept is - c/m
now since m is negative , c has to be postive to make the intercept postive
r+5m
1) m = -5
r -25
no idea about r
2) r > 0
still no clue
togther too we cannot find...
IMO E
1. the slope of line k is -5
2. r > 0
equation of a line
Y = MX + C
given that m = -ve
r = -5m + c
c = r+5m
x intercept is - c/m
now since m is negative , c has to be postive to make the intercept postive
r+5m
1) m = -5
r -25
no idea about r
2) r > 0
still no clue
togther too we cannot find...
IMO E
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Hi All,
We're told that in the xy-plane, Line K has a NEGATIVE SLOPE and passes through the point (-5, R). We're asked if the X-intercept of line K is positive. This is a YES/NO question. The answer to this question depends on the Slope of Line K and the value of R, meaning that we can TEST VALUES to answer it.
1) The slope of line K is -5.
While a slope of -5 is somewhat 'steep', we still don't know the value of R, so Line K may or may not have a positive X-intercept.
IF....
R = 1, then Line K will have a NEGATIVE X-intercept and the answer to the question is NO.
R = 1000, then Line K will have a POSITIVE X-intercept and the answer to the question is YES.
Fact 1 is INSUFFICIENT
2) R > 0
Fact 2 tells us nothing about the SLOPE of Line K, but both TESTs from Fact 1 can be used in Fact 2 IF the slope of Line K = -5:
IF....
Slope = -5 and....
R = 1, then Line K will have a NEGATIVE X-intercept and the answer to the question is NO.
R = 1000, then Line K will have a POSITIVE X-intercept and the answer to the question is YES.
Fact 2 is INSUFFICIENT
Combined, we already have 2 TESTs that 'fit' both Facts and gives us different answers (one "NO" and one "YES"), so no additional work is needed.
Combined, INSUFFICIENT
Final Answer: E
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Rich
We're told that in the xy-plane, Line K has a NEGATIVE SLOPE and passes through the point (-5, R). We're asked if the X-intercept of line K is positive. This is a YES/NO question. The answer to this question depends on the Slope of Line K and the value of R, meaning that we can TEST VALUES to answer it.
1) The slope of line K is -5.
While a slope of -5 is somewhat 'steep', we still don't know the value of R, so Line K may or may not have a positive X-intercept.
IF....
R = 1, then Line K will have a NEGATIVE X-intercept and the answer to the question is NO.
R = 1000, then Line K will have a POSITIVE X-intercept and the answer to the question is YES.
Fact 1 is INSUFFICIENT
2) R > 0
Fact 2 tells us nothing about the SLOPE of Line K, but both TESTs from Fact 1 can be used in Fact 2 IF the slope of Line K = -5:
IF....
Slope = -5 and....
R = 1, then Line K will have a NEGATIVE X-intercept and the answer to the question is NO.
R = 1000, then Line K will have a POSITIVE X-intercept and the answer to the question is YES.
Fact 2 is INSUFFICIENT
Combined, we already have 2 TESTs that 'fit' both Facts and gives us different answers (one "NO" and one "YES"), so no additional work is needed.
Combined, INSUFFICIENT
Final Answer: E
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We need to determine whether the x-intercept of line k is positive, given that line k has a negative slope and passes through the point (-5, r).beater wrote:In the xy-plane, if line k has negative slope and passes through the point (-5,r), is the x intercept of line k positive?
1. the slope of line k is -5
2. r > 0
We can let the slope of line k be m and the x-intercept of line k be a; that is, line k passes through the point (a, 0). Using the slope formula m = (y2 - y1)/(x2 - x1), we have:
m = (0 - r)/(a -(-5))= -r/(a + 5)
Statement One Alone:
The slope of line k is -5.
Using the information in statement one, we can say the following:
-r/(a + 5) = -5
a + 5 = r/5
a = r/5 - 5
Since we don't know the value of r, we cannot determine the value of a.
For example, if r = 5, a = -4, which is negative. However, if r = 50, a = 5, which is positive. Statement one alone is not sufficient to answer the question.
Statement Two Alone:
r > 0
Knowing r is positive does not give us enough information to determine whether a, the x-intercept of line k, is positive. Statement two alone is not sufficient to answer the question.
Statements One and Two Together:
Looking at our work from statement one, and keeping in mind that r > 0 from statement two, we see that a can be positive or negative.
For example, if r = 5 then a = -4, which is negative. However, if r = 50 then a = 5, which is positive. The two statements together are still not sufficient to answer the question.
Answer: E
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