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The line ‘p’ passes through origin and has slope 3. If the points (x,

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The line ‘p’ passes through origin and has slope 3. If the points (x,  [#permalink]

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New post 07 Oct 2018, 10:38
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Question Stats:

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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

EG-2

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The line ‘p’ passes through origin and has slope 3. If the points (x,  [#permalink]

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New post 07 Oct 2018, 12:39
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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

EG-2


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

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The line ‘p’ passes through origin and has slope 3. If the points (x,  [#permalink]

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New post 08 Oct 2018, 11:13
1
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

EG-2

Use the slope-intercept form of the equation of a line.
To find variables, either plug in each numeric coordinate or treat the coordinate pairs as a function.

(1) Write the equation of Line P in slope-intercept form:
\(y=mx+b\)
\(m=\) slope
\(b=\) y-intercept

If a line passes through the origin, its y-intercept is 0
(as is its x-intercept, but that is not part of this equation)

Line P:
\(y=3x+0\) =>
\(y=3x\)

(2) Find the variables
Plug numeric values from each pair of coordinates into the equation*

-- \((x, 12)\)
\(y=3x\)
\(12=3x\)
\(x=4\)

-- \((6, y)\)
\(y=3x\)
\(y=3*(6)\)
\(y=18\)

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

Answer A

*OR use the linear function \(y=3x\) and do mental math
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Re: The line ‘p’ passes through origin and has slope 3. If the points (x,  [#permalink]

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New post 10 Oct 2018, 17:47
1
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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Re: The line ‘p’ passes through origin and has slope 3. If the points (x, &nbs [#permalink] 10 Oct 2018, 17:47
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