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In the coordinate plane, Line A has a slope of 1 and an xintercept
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12 Oct 2015, 21:57
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In the coordinate plane, Line A has a slope of 1 and an xintercept of 1. Line B has a slope of 2 and a yintercept of 2. If the two lines intersect at the point (a,b), what is the sum a+b? A. 0 B. 1 C. 2 D. 3 E. 4 Kudos for a correct solution.
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In the coordinate plane, Line A has a slope of 1 and an xintercept
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12 Oct 2015, 23:28
Bunuel wrote: In the coordinate plane, Line A has a slope of 1 and an xintercept of 1. Line B has a slope of 2 and a yintercept of 2. If the two lines intersect at the point (a,b), what is the sum a+b?
A. 0 B. 1 C. 2 D. 3 E. 4
Kudos for a correct solution. General Equation of Line is given by, y = mx +c where m is slope of line and c is YInterceptEquation of Line A, y = x + c where c is YIntercept but since Line A passes through (1, 0) [For x intercept =1, y must be 0], so 0 = 1+c i.e. c = 1 hence, Equation of Line A, y = x + 1Equation of Line B, y = 2x  2For point of Intersection of Line A and Line B x + 1 = 2x  2 i.e. x = 1 and y = 0 i.e. (a, b) = (1, 0) i.e. a+b = 1 Answer: option B
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Re: In the coordinate plane, Line A has a slope of 1 and an xintercept
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13 Oct 2015, 06:24
IMO answer is 1.
equation 1: y=x+1 equation 2: y=2x2



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Re: In the coordinate plane, Line A has a slope of 1 and an xintercept
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13 Oct 2015, 07:54
So first of all, find the equations of both lines.
Line A: Slope=1, X Intercept =1.
Find the Y Intercept
X Int=b/1=1 b=1 b=1
Line A: Y=X+1
Line B Slope=2, Y Intercept=2
Line B Y=2X2
X+1=2X2 3=3X X=1
Plug X into any equation, Y=0
The answer is A



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Re: In the coordinate plane, Line A has a slope of 1 and an xintercept
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13 Oct 2015, 19:31
Bunuel wrote: In the coordinate plane, Line A has a slope of 1 and an xintercept of 1. Line B has a slope of 2 and a yintercept of 2. If the two lines intersect at the point (a,b), what is the sum a+b?
A. 0 B. 1 C. 2 D. 3 E. 4
Kudos for a correct solution. Equation of line 1 y=mx+c =>y=x+c It passes through point (1,0) hence 0=1+c =>c=1 equation of line 1 becomes y=x+1 =>y+x=1 it will also pass through point (a,b) hence a+b=1 We don't need the equation of line in this case . Ans: B
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Re: In the coordinate plane, Line A has a slope of 1 and an xintercept
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18 Oct 2015, 12:32
Bunuel wrote: In the coordinate plane, Line A has a slope of 1 and an xintercept of 1. Line B has a slope of 2 and a yintercept of 2. If the two lines intersect at the point (a,b), what is the sum a+b?
A. 0 B. 1 C. 2 D. 3 E. 4
Kudos for a correct solution. VERITAS PREP OFFICIAL SOLUTION:When attempting to find where two lines intersect, it is typically best to get the lines in pointslope form (y = mx + b). For Line A, you know that the slope is 1, so you have a head start in that m = 1. So you're starting with y = x + b. And then remember  the xintercept is the point at which y = 0, so that point is (1, 0). You can then plug that point into the equation to find b: 0 = (1) + b, so b = 1. You know now that Line A has the equation y = x + 1. For Line B, you know that the slope is 2 (so y = 2x + b) and that when x is 0, y = 2. Plug that into the line equation to solve for b and you have 2 = 2(0) + b, so b = 2. Now you know the equation for Line B: y = 2x + 4. Since y = x + 1 and y = 2x + 4, the two lines will intersect where x + 1 = 2x + 4. Algebraically that leads you to 3 = 3x, so x = 1. Plug that back into either line to find y, and you'll find that y = 2. Since the point of intersection is (1, 2), the sum a+b=1, making B the correct answer.
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Re: In the coordinate plane, Line A has a slope of 1 and an xintercept
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05 May 2017, 18:52
Bunuel wrote: Bunuel wrote: In the coordinate plane, Line A has a slope of 1 and an xintercept of 1. Line B has a slope of 2 and a yintercept of 2. If the two lines intersect at the point (a,b), what is the sum a+b?
A. 0 B. 1 C. 2 D. 3 E. 4
Kudos for a correct solution. VERITAS PREP OFFICIAL SOLUTION:When attempting to find where two lines intersect, it is typically best to get the lines in pointslope form (y = mx + b). For Line A, you know that the slope is 1, so you have a head start in that m = 1. So you're starting with y = x + b. And then remember  the xintercept is the point at which y = 0, so that point is (1, 0). You can then plug that point into the equation to find b: 0 = (1) + b, so b = 1. You know now that Line A has the equation y = x + 1. For Line B, you know that the slope is 2 (so y = 2x + b) and that when x is 0, y = 2. Plug that into the line equation to solve for b and you have 2 = 2(0) + b, so b = 2. Now you know the equation for Line B: y = 2x + 4. Since y = x + 1 and y = 2x + 4, the two lines will intersect where x + 1 = 2x + 4. Algebraically that leads you to 3 = 3x, so x = 1. Plug that back into either line to find y, and you'll find that y = 2. Since the point of intersection is (1, 2), the sum a+b=1, making B the correct answer. Two questions: 1. Is it incorrect to assume that a given y intercept can be written as is into the equation? That is, for line 2, I and everyone who wrote numbers into the equations wrote (given that slope is 2 and y intercept is 2): y = 2x2 Coordinate geometry was a long time ago. Have I forgotten something? Are we incorrect to write the equation in the way that we did? Because 2. The official solution has the line as y = 2x+4. I'm lost. I would interpret that to mean that when x is 0, the y intercept is .... 4? Posted from my mobile device
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Re: In the coordinate plane, Line A has a slope of 1 and an xintercept
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15 Jun 2017, 21:32
Bunuel wrote: In the coordinate plane, Line A has a slope of 1 and an xintercept of 1. Line B has a slope of 2 and a yintercept of 2. If the two lines intersect at the point (a,b), what is the sum a+b?
A. 0 B. 1 C. 2 D. 3 E. 4
Kudos for a correct solution. Quite simply, you just need to set both equations equal in this problem and then plug in the value of x into both equations ( well it's not actually necessary to plug into both because if they equations are equal then x plugged into either will give you the same value for y but sometimes its fine to double check) in order to solve for X. Secondly, you just take the sum of the x and y value and you have the answer. 2x2 = x +1 3x= 3 x = 1 2(1)2= 0 so "y" is 0 (1) +1 = 0 same thing 1 + 0 = 0 Thus B



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Re: In the coordinate plane, Line A has a slope of 1 and an xintercept
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31 Aug 2019, 01:31
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Re: In the coordinate plane, Line A has a slope of 1 and an xintercept
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