coordinate

Substitute the two points in the equation and solve.

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.

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

Good point !
I had just been studying Geometry ... and all the geometry concepts were running through my mind.
Agree that it is quicker using algebra here ! Thanks.

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