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Difficulty:
25%
(medium)
Question Stats:
78% (01:54) correct
22%
(01:46)
wrong
based on 963
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In the xy-plane, line a and line b have the same slope. If the y-intercept of line a is -1, what is the y-intercept of line b ?
(1) The x-intercept of line a is -1.
(2 Line b passes through the point (10, 20).
(1) The x-intercept of line a is -1.
(2 Line b passes through the point (10, 20).
24 Apr 2012, 21:46
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monir6000
In the xy-plane, line a and line b have the same slope. If the y-intercept of line a is -1, what is the y-intercept of line b ?
You don't need any algebra or even drawing, to solve this question. Just try to visualize the info given. First of all notice that "line a and line b have the same slope" means that the lines are parallel.
(1) The x-intercept of line a is -1. We have two points of line a: (0, -1) and (-1, 0), so it's fixed (we can find its equation). But since there are infinitely many parallel lines to line a, then each will have different y-intercept. Not sufficient.
(2 Line b passes through the point (10, 20). We have one point of line a: (0, -1) and one point of line b: (10, 20). We can rotate two parallel lines around these points, which will give different y-intercept of line b. Not sufficient.
(1)+(2) We have fixed line a, and its parallel line b which passes through the point (10, 20), which means that line b is also fixed and we can find its y-intercept (through some particular point, you can draw only one line which will be parallel to some fixed line). Sufficient.
Answer: C.
harshavmrg
Joined: 25 Feb 2010
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24 Apr 2012, 21:39
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monir6000
given that line a and b are having the same slope... and given the line a y-intercept is -1...we need to find y-intercept of line b
1) x intercept of line a is -1
any line equation is given by y=mx+a for line a
y=mx+b for line b
hence the equation becomes y = mx - 1
for x intercept y becomes 0
0 = mx - 1
mx = 1
so for x intercept to be - 1 then to make that happen x = 1/m = -1
so m should be -1
but this makes the line b equation as y = -x + b
beyond this we cant find... hence not sufficient.. so A and D options are off...
2) line b passes through (10, 20)
y = mx + b
so 20 = 10m + b
two unknowns...we cannot solve
together.. we know that m = - 1 and 20 = 10m + b
so 20 = -10 + b
b = 30 which is the y-intercept of line b
hence C
