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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

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by BTGmoderatorDC » Sun Jan 19, 2020 7:11 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



OA B

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Re: 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

by Jay@ManhattanReview » Sun Jan 19, 2020 8:41 pm
BTGmoderatorDC wrote: ↑
Sun Jan 19, 2020 7:11 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

OA B

Source: Veritas Prep
Say the equation of a line is y = mx + c, where m = slope/magnitude of the line and c = y-intercept

Line A:

Given the equation of the line is y = mx + c, we have m = –1; thus, the equation is y = –x + c. We can rewrite y = –x + c as x = –y + c, where c = x-intercept. So, c = 1 (given).

Thus, the equation of Line A: y = –x + 1 --- (1)

Line B:

Given the equation of the line is y = mx + c, we have m = 2 and c = –2; thus, the equation is y = 2x – 2.

Thus, the equation of Line B: y = 2x – 2 --- (2)

Equating equation (1) and (2), we have

–x + 1 = 2x – 2 => x = 1 => y = –x + 1 = –1 + 1 = 0. Or, the he two lines intersect at the point (1, 0). Thus, a + b = 1 + 0 = 1.

The correct answer: B

Hope this helps!

-Jay
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