In the XY-coordinate system, if (a,b) and (a+3, b+ K) are two points on the line defined by the equation X=3Y-7, then K=
A) 9
B) 3
C) 7/3
D) 1
E) 1/3
-thanx
A) 9
B) 3
C) 7/3
D) 1
E) 1/3
-thanx
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Source: Beat The GMAT — Problem Solving |
ok ... we know that an equation of line is y=mx+c, where m is the gradient/slope and c is the y-intercept.
The question provide: X=3Y-7.
We need to firstly get this in the format of y=mx+c
so x=3y-7 can be rearranged:
x=3y-7
x+7=3y
(x+7)/3 = y
So y=1/3x + 7/3
we know can easily tell that the y-intercept is 7/3.
So we have one coordinate which fits the line equation. This coordinate is (0,7/3).
If we find the x-intercept, then we will have another coordinate to play with. So substitute a value of 0 for y in the equation:
0=1/3x + 7/3
-7/3=1/3x
-7/3*3/1=x
-21/3=x
x=-7.
So we have another coordinate (-7,0) which fits the equation.
This second coordinate is easier to work with ... so lets take this one forward:
The question mentions (a,b) and (a+3,b+K) being 2 points on the line.
So we have established that (-7,0) is one of these points.
So the 2nd point on the line is (-7+3,0+k) or (-4,0+k)
Lets substitute these values (x=-4, y=0+k) into the equation:
y=1/3x+7/3
0+k=1/3(-4)+7/3
k=-4/3+7/3
k=3/3
k=1
So the answer is D.
What is the official answer please ? And where is this question from ?
Thanks.
The question provide: X=3Y-7.
We need to firstly get this in the format of y=mx+c
so x=3y-7 can be rearranged:
x=3y-7
x+7=3y
(x+7)/3 = y
So y=1/3x + 7/3
we know can easily tell that the y-intercept is 7/3.
So we have one coordinate which fits the line equation. This coordinate is (0,7/3).
If we find the x-intercept, then we will have another coordinate to play with. So substitute a value of 0 for y in the equation:
0=1/3x + 7/3
-7/3=1/3x
-7/3*3/1=x
-21/3=x
x=-7.
So we have another coordinate (-7,0) which fits the equation.
This second coordinate is easier to work with ... so lets take this one forward:
The question mentions (a,b) and (a+3,b+K) being 2 points on the line.
So we have established that (-7,0) is one of these points.
So the 2nd point on the line is (-7+3,0+k) or (-4,0+k)
Lets substitute these values (x=-4, y=0+k) into the equation:
y=1/3x+7/3
0+k=1/3(-4)+7/3
k=-4/3+7/3
k=3/3
k=1
So the answer is D.
What is the official answer please ? And where is this question from ?
Thanks.
-
simplyjat
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You do not need to do all the calculations to find (-7,0) and (0,7/3).
This question can be easily solved by algebra X = 3Y -7
a = 3b - 7
=> 3b - a = 7
and
(a+3) = 3(b+k) -7
=> a + 3 = 3b + 3k -7
=> 3 = (3b-a) + 3k -7
=> 3 = 7 + 3k -7
=> 3k = 3
=> k = 1
This question can be easily solved by algebra X = 3Y -7
a = 3b - 7
=> 3b - a = 7
and
(a+3) = 3(b+k) -7
=> a + 3 = 3b + 3k -7
=> 3 = (3b-a) + 3k -7
=> 3 = 7 + 3k -7
=> 3k = 3
=> k = 1
simplyjat
i think subtitution wont give correct ans all the times...
In the XY-coordinate system, if (a,b) and (a+3, b+ K) are two points on the line defined by the equation X=3Y-7, then K=
A) 9
B) 3
C) 7/3
D) 1
E) 1/3
write the equation x=3y-7 in the y=mx+c format and find ou the slope
y=1/3x+7
m=1/3 which is slope and then by using slope formula
m=y2-y1/x2-x1
substitute 2 points in the above formula and then equate the slope...
1/3=b+k-b/a+3-A
K=1. is the ans
In the XY-coordinate system, if (a,b) and (a+3, b+ K) are two points on the line defined by the equation X=3Y-7, then K=
A) 9
B) 3
C) 7/3
D) 1
E) 1/3
write the equation x=3y-7 in the y=mx+c format and find ou the slope
y=1/3x+7
m=1/3 which is slope and then by using slope formula
m=y2-y1/x2-x1
substitute 2 points in the above formula and then equate the slope...
1/3=b+k-b/a+3-A
K=1. is the ans
