X-Y PLANE

[danjuma]

If the line k in the xy plane has slope of -3/2, does line k pass through the point (12, -13)?

a.The point (6, -2) lies on line k

b. The point (2, 4) lies on line k.

Is there an easy way of working this out using Y=MX + B?

Thanks a million times, Danju

[beat_gmat_09]

Plug in the values of x, y pair in the equation you mentioned. You'll get each statement is sufficient.
Answer D.

[Geva@EconomistGMAT]

Think about what it means that a point such (12, -13) lies on the line k: it means that the line's equation y=mx +b is such that if x=12, y must equal -13. You also know that the slope (which is the m in the equation) is -3/2, so the equation is y=-3x/2+b. Bascially, all you need is b: if you know b, then you know the line's equation, and you could then plug in x=12 and see whether or not comes out as -13. thus, the key is finding b.

Each of the statements allows you to find b, by using the same logic:

If (6,-2) lies on the line, then if we plug in x=6 into the line's equation y=-3x/2+b, y should equal -2. Plug these into the equation, and get
-2=-3/2*6+b
A single equation with b, which will allow you to find b. From there, you will be able to know a definite answer as to whether the point 12, -13 satisfies the equation or not, so the statement is sufficient. You don't need to work out everything to know that you will have a single answer to the question stem: either a yes or a no. The same thing can be done with stat. (2), which will also be sufficient. The answer is D, and you can move on to the next question.

Just to illustrate, let's solve for b above:
b=-2 + 3/2 * 6 = -2+9 = 7.
thus, the equation of line k is y=-3x/2+7.
So, does the point 12, -13 lie on the line? Let's see: plug in x=12 into the line equation, and see if the result is -13:
y=-3*12/2 + 7
y=-18+7 = -11
So y does not come out as -13, and the answer to the question stem is a definite "no" - but that is sufficient, as you are able to answer the question.

The same process can be done with stat. (2)