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

Question

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 .

GMATinsight · Accepted Answer

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)  , 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

longfellow · Answer

IMO answer is 1.

equation 1: y=-x+1
equation 2: y=2x-2

jmikery · Answer

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

thembaseeker · Answer

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

Bunuel · Answer

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 - 2.

Since y = -x + 1 and y = 2x - 2, the two lines will intersect where -x + 1 = 2x - 2. Algebraically that leads you to x = 1. Plug that back into either line to find y, and you'll find that y = 0. Since the point of intersection is (1, 0), the sum a+b=1, making B the correct answer.

Nunuboy1994 · Answer

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 
 B

TheBunk · Answer

I am confused here. Why line B equation is y = 2x +4 ? We are given the slope (2) and the y-intercept (-2). Shouldn't the equation be y = 2x - 2 ?

Bunuel · Answer

Yes, the OE had typos. Edited. Thank you!

MathRevolution · Answer

Equation of line is y = mx + c or x = my + c

For line A: m = -1 and the x-intercept is 1

=> x = (-1)y + 1

=> x + y = 1---------------(1)

For line B: m = 2 and the y-intercept is -2

=> y = (2)x - 2

=> 2x + y = 2---------------(1)

Both line intersects at (a,b). Therefore, lets find value of x and y:

=> x + x + y = 2

=> x + 1 = 2

=> x = 1 and therefore y = 0

=> (x,y) ---> ( 1 , 0 )---->(a,b)-----> (a + b) -----> ( 1  +  0  = 1)

Answer B

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards