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

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

by GMATinsight » Mon Oct 12, 2015 10:50 pm
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

Answer: Option B
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by GMATinsight » Mon Oct 12, 2015 10:50 pm
GMATinsight 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

Answer: Option B
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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