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In the xy plane, which of the statements below individually [#permalink]
16 Dec 2019, 10:07
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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 yintercept of line z is 0. [C] For any point (a, b) on line z, a = b.
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Re: In the xy plane, which of the statements below individually [#permalink]
16 Dec 2019, 10:10
OFFICIAL EXPLANATION: Statement I tells you directly that b, the yintercept, is equal to 0. Thus, the line passes through the origin. For statement II, both the slope and the yintercept could be 0, in which case line z is a horizontal line lying on the xaxis and therefore passes through the origin. Or, the slope and yintercept could simply be opposites, such as 2 and 2. A line with a yintercept 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.
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Re: In the xy plane, which of the statements below individually [#permalink]
22 Jun 2020, 17:52
huda wrote: OFFICIAL EXPLANATION:
Statement I tells you directly that b, the yintercept, is equal to 0. Thus, the line passes through the origin.
For statement II, both the slope and the yintercept could be 0, in which case line z is a horizontal line lying on the xaxis and therefore passes through the origin. Or, the slope and yintercept could simply be opposites, such as 2 and 2. A line with a yintercept 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?
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Re: In the xy plane, which of the statements below individually [#permalink]
23 Jun 2020, 06:00
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Farina wrote: huda wrote: OFFICIAL EXPLANATION:
Statement I tells you directly that b, the yintercept, is equal to 0. Thus, the line passes through the origin.
For statement II, both the slope and the yintercept could be 0, in which case line z is a horizontal line lying on the xaxis and therefore passes through the origin. Or, the slope and yintercept could simply be opposites, such as 2 and 2. A line with a yintercept 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? Key concept: If a point lies ON a line, then the coordinates of that point must SATISFY the equation of that line.Statement 3: For any point (a, b) on line z, a = bThis tells us that all points on the line are such that the absolute value of the xcoordinate = the absolute value of the ycoordinate. In other words, x = y So, for example, since 3 = 3, we know that the point (3, 3) lies on line z Likewise, since 0 = 0, we know that the point (0, 0) lies on line z In other words, line z passes through the origin Cheers, Brent
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Re: In the xy plane, which of the statements below individually [#permalink]
23 Jun 2020, 16:41
Thank you for your reply. Just want to add that 0 is one possibility, the value could be any number right? in that case statement 3 shouldnt be the confirmed answer? GreenlightTestPrep wrote: Farina wrote: huda wrote: OFFICIAL EXPLANATION:
Statement I tells you directly that b, the yintercept, is equal to 0. Thus, the line passes through the origin.
For statement II, both the slope and the yintercept could be 0, in which case line z is a horizontal line lying on the xaxis and therefore passes through the origin. Or, the slope and yintercept could simply be opposites, such as 2 and 2. A line with a yintercept 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? Key concept: If a point lies ON a line, then the coordinates of that point must SATISFY the equation of that line.Statement 3: For any point (a, b) on line z, a = bThis tells us that all points on the line are such that the absolute value of the xcoordinate = the absolute value of the ycoordinate. In other words, x = y So, for example, since 3 = 3, we know that the point (3, 3) lies on line z Likewise, since 0 = 0, we know that the point (0, 0) lies on line z In other words, line z passes through the origin Cheers, Brent
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Re: In the xy plane, which of the statements below individually [#permalink]
23 Jun 2020, 17:09
Farina wrote: Thank you for your reply. Just want to add that 0 is one possibility, the value could be any number right? in that case statement 3 shouldnt be the confirmed answer?
A line is just a graphical representation of all possible solutions to an equation. That is, the x and ycoordinates of every point on a line satisfy the equation of that line. So, for example, the equation y = x + 1 has infinitely many solutions, including (0,1), (1,2), (2,3), (3.97, 4.97), etc. For more on this concept watch: https://www.greenlighttestprep.com/modu ... /video/996Likewise, the equation x = y also has infinitely many solutions. One of those solutions is (0, 0) since x = 0 and y = 0 satisfies the equation x = y In fact any pair of values that satisfy the equation will be on the line.
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Re: In the xy plane, which of the statements below individually
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