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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