y = mx + b

slope = (difference in y)/(difference in x)

we are given these two points are on line p, they share the same slope and it passes through the origin so (0,0) is one point.

(12 - 0)/(x - 0) = 3
3x = 12
x = 4

(y - 0)/(6 - 0) = 3
y = 18

x - 2y = 4 - (2*18) = 4 - 36 = -32

Answer choice A

Posted from my mobile device

The formula for slope is: (y2 - y1) / (x2 - x1). Since the slope of the given line is 3, we have:

(y - 12)/(6 - x) = 3

y - 12 = 18 - 3x

3x + y = 30

Since the line also passes through the origin, we have:

(y - 0)/(6 - 0) = 3

y/6 = 3

y = 18

Since y = 18, then 3x + 18 = 30 gives us x = 4. So x - 2y = 4 - 2(18) = 4 - 36 = -32.

Alternate Solution:

We know that lines that pass through the origin have the form y = mx where m is the slope. Since the slope is given to be 3, the equation of line p is y = 3x. Since each of the points (x, 12) and (6, y) are on this line, they must satisfy the equation of the line. Thus, we have

12 = 3x

x = 4

and

y = 3(6)

y = 18

Thus, x - 2y = 4 - 2(18) = 4 - 36 = -32.

Answer: A
_________________