SajjadAhmad wrote:
The line ‘p’ passes through origin and has slope 3. If the points (x, 12) and (6, y) lie on ‘p’, what is the value of x - 2y?
A. -32
B. -20
C. -18
D. 18
E. 32
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
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