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

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Senior RC Moderator
Joined: 02 Nov 2016
Posts: 4447
GPA: 3.39
The line ‘p’ passes through origin and has slope 3. If the points (x,  [#permalink]

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07 Oct 2018, 11:38
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15% (low)

Question Stats:

88% (01:25) correct 12% (01:48) wrong based on 40 sessions

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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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07 Oct 2018, 13:39
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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

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

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Senior SC Moderator
Joined: 22 May 2016
Posts: 3682
The line ‘p’ passes through origin and has slope 3. If the points (x,  [#permalink]

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08 Oct 2018, 12:13
1
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) $$(x - 2y)=$$?
$$4 - (2*18)=$$
$$(4-36)=-32$$

*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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10 Oct 2018, 18:47
1
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.

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Re: The line ‘p’ passes through origin and has slope 3. If the points (x,   [#permalink] 10 Oct 2018, 18:47
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