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In the coordinate plane, Line A has a slope of -1 and an x-intercept

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In the coordinate plane, Line A has a slope of -1 and an x-intercept  [#permalink]

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New post 12 Oct 2015, 21:57
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A
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Question Stats:

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In the coordinate plane, Line A has a slope of -1 and an x-intercept  [#permalink]

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New post 12 Oct 2015, 23:28
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Bunuel wrote:
In the coordinate plane, Line A has a slope of -1 and an x-intercept of 1. Line B has a slope of 2 and a y-intercept 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 Y-Intercept

Equation of Line A, y = -x + c where c is Y-Intercept
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 + 1

Equation of Line B, y = 2x - 2

For 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 x-intercept  [#permalink]

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New post 13 Oct 2015, 06:24
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IMO answer is 1.

equation 1: y=-x+1
equation 2: y=2x-2
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Re: In the coordinate plane, Line A has a slope of -1 and an x-intercept  [#permalink]

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New post 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=2X-2

-X+1=2X-2
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 x-intercept  [#permalink]

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New post 13 Oct 2015, 19:31
Bunuel wrote:
In the coordinate plane, Line A has a slope of -1 and an x-intercept of 1. Line B has a slope of 2 and a y-intercept 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 :-D .

Ans: B
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Re: In the coordinate plane, Line A has a slope of -1 and an x-intercept  [#permalink]

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New post 18 Oct 2015, 12:32
Bunuel wrote:
In the coordinate plane, Line A has a slope of -1 and an x-intercept of 1. Line B has a slope of 2 and a y-intercept 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 point-slope 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 x-intercept 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 x-intercept  [#permalink]

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New post 05 May 2017, 18:52
Bunuel wrote:
Bunuel wrote:
In the coordinate plane, Line A has a slope of -1 and an x-intercept of 1. Line B has a slope of 2 and a y-intercept 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 point-slope 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 x-intercept 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 = 2x-2

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?

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Re: In the coordinate plane, Line A has a slope of -1 and an x-intercept  [#permalink]

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New post 15 Jun 2017, 21:32
Bunuel wrote:
In the coordinate plane, Line A has a slope of -1 and an x-intercept of 1. Line B has a slope of 2 and a y-intercept 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.

2x-2 = -x +1
3x= 3
x = 1

2(1)-2= 0 so "y" is 0
-(1) +1 = 0 same thing

1 + 0 = 0

Thus
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Re: In the coordinate plane, Line A has a slope of -1 and an x-intercept  [#permalink]

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Re: In the coordinate plane, Line A has a slope of -1 and an x-intercept   [#permalink] 31 Aug 2019, 01:31
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