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In the xy plane, which of the statements below individually
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16 Dec 2019, 10:07
16 Dec 2019, 10:07
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68% (01:17) correct
31% (00:56) wrong based on 57 sessions
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In the xy plane, which of the statements below individually provide enough information to determine whether line z passes through the origin?
Indicate all such statements.
[A] The equation of line z is y = mx + b and b = 0.
[B] The sum of the slope and the y-intercept of line z is 0.
[C] For any point (a, b) on line z, |a| = |b|.
Indicate all such statements.
[A] The equation of line z is y = mx + b and b = 0.
[B] The sum of the slope and the y-intercept of line z is 0.
[C] For any point (a, b) on line z, |a| = |b|.
Re: In the xy plane, which of the statements below individually
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16 Dec 2019, 10:10
16 Dec 2019, 10:10
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OFFICIAL EXPLANATION:
Statement I tells you directly that b, the y-intercept, is equal to 0. Thus, the line passes through the origin.
For statement II, both the slope and the y-intercept could be 0, in which case line z is a horizontal line lying on the x-axis and therefore passes through the origin. Or, the slope and y-intercept could simply be opposites, such as 2 and -2. A line with a y-intercept of -2 and a slope of 2 would not pass through the origin. Therefore, this statement is not sufficient to determine whether line z passes through the origin.
As for statement III, since |a| = |b| must hold for every point on the line, then (0, 0) is a point on the line, since |0| = |0|.
Statement I tells you directly that b, the y-intercept, is equal to 0. Thus, the line passes through the origin.
For statement II, both the slope and the y-intercept could be 0, in which case line z is a horizontal line lying on the x-axis and therefore passes through the origin. Or, the slope and y-intercept could simply be opposites, such as 2 and -2. A line with a y-intercept of -2 and a slope of 2 would not pass through the origin. Therefore, this statement is not sufficient to determine whether line z passes through the origin.
As for statement III, since |a| = |b| must hold for every point on the line, then (0, 0) is a point on the line, since |0| = |0|.
Re: In the xy plane, which of the statements below individually
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22 Jun 2020, 17:52
22 Jun 2020, 17:52
huda wrote:
OFFICIAL EXPLANATION:
Statement I tells you directly that b, the y-intercept, is equal to 0. Thus, the line passes through the origin.
For statement II, both the slope and the y-intercept could be 0, in which case line z is a horizontal line lying on the x-axis and therefore passes through the origin. Or, the slope and y-intercept could simply be opposites, such as 2 and -2. A line with a y-intercept of -2 and a slope of 2 would not pass through the origin. Therefore, this statement is not sufficient to determine whether line z passes through the origin.
As for statement III, since |a| = |b| must hold for every point on the line, then (0, 0) is a point on the line, since |0| = |0|.
Statement I tells you directly that b, the y-intercept, is equal to 0. Thus, the line passes through the origin.
For statement II, both the slope and the y-intercept could be 0, in which case line z is a horizontal line lying on the x-axis and therefore passes through the origin. Or, the slope and y-intercept could simply be opposites, such as 2 and -2. A line with a y-intercept of -2 and a slope of 2 would not pass through the origin. Therefore, this statement is not sufficient to determine whether line z passes through the origin.
As for statement III, since |a| = |b| must hold for every point on the line, then (0, 0) is a point on the line, since |0| = |0|.
For statement 3, why did you consider |a| and |b| = 0?
