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In the xy-plane, if line k passes through the points (3, -4) and (a,b)

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In the xy-plane, if line k passes through the points (3, -4) and (a,b) [#permalink] New post   04 Sep 2019, 23:10
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In the xy-plane, if line k passes through the points (3, -4) and (a, b), where b = 4a - 16 and a > 3 what is the slope of k?

A. -4
B. -1/2
C. 0
D. 2
E. 4
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E
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rishinric
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Re: In the xy-plane, if line k passes through the points (3, -4) and (a,b) [#permalink] New post   04 Sep 2019, 23:24
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In the xy-plane, if line k passes through the points (3, -4) and (a, b), where b = 4a - 16 and a > 3 what is the slope of k?

A. -4
B. -1/2
C. 0
D. 2
E. 4

If A is 4 then b is 0, Point will be (4,0)
Now slope = (0+4)/(4-3) = 4
If A is 6 then b is 8, Point will be (6,8)
Now slope = (8+4)/(6-3) = 4
So answer is E

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Re: In the xy-plane, if line k passes through the points (3, -4) and (a,b) [#permalink] New post   04 Sep 2019, 23:38
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In the xy-plane, if line k passes through the points (3, -4) and (a, b), where b = 4a - 16 and a > 3 what is the slope of k?

if a=4 , b=0
if a=5, b=4

slope=\(\frac{-4-0}{3-4}=\frac{-4}{-1}=4\)
slope=\(\frac{-4-4}{3-5}=\frac{-8}{-2}=4\)
therefore, E
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Re: In the xy-plane, if line k passes through the points (3, -4) and (a,b) [#permalink] New post   05 Sep 2019, 00:11
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In the xy-plane, if line k passes through the points (3, -4) and (a, b), where b = 4a - 16 and a > 3 what is the slope of k?

A. -4
B. -1/2
C. 0
D. 2
E. 4

points (3, -4) and (a, b) where b = 4a - 16 and a > 3

if a=4, b=0

Points would be (3, -4) and (4, 0)
Slope of line=\(\frac{y2-y1}{x2-x1}\) =\(\frac{0+4}{4-3}\) = 4........option E

P.S: take any value of a (a>3), you'll get same slope.
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Re: In the xy-plane, if line k passes through the points (3, -4) and (a,b) [#permalink] New post   05 Sep 2019, 00:21
The generic equation of a line is y=mx+c
From the question stem, we know that a>3
Hence the slope cannot be negative and it cannot be 0 either.
Testing with m=2
y=2x+c
Plugging in (3,-4)
-4=2*3+c hence c= -10
y=2x-10
The x intercept has to be more than 3 if the equation of the line is correct
0=2x-10 meaning x=5.
Hence the slope is 2.

The answer is therefore D.

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Re: In the xy-plane, if line k passes through the points (3, -4) and (a,b) [#permalink] New post   05 Sep 2019, 01:12
for (a,b) b = 4a - 16 and a > 3
a=4 , b=0
m=y2-y1/x2-x1 ; -4/-1 ; 4
IMO E ; 4


In the xy-plane, if line k passes through the points (3, -4) and (a, b), where b = 4a - 16 and a > 3 what is the slope of k?

A. -4
B. -1/2
C. 0
D. 2
E. 4
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Re: In the xy-plane, if line k passes through the points (3, -4) and (a,b) [#permalink] New post   05 Sep 2019, 04:12
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Quote:
In the xy-plane, if line k passes through the points (3, -4) and (a, b), where b = 4a - 16 and a > 3 what is the slope of k?

A. -4
B. -1/2
C. 0
D. 2
E. 4


\(points(x,y): (3,-4);(a,4a-16)\)
\(slope(m)=\frac{y2-y1}{x2-x1}=\frac{4a-16-(-4)}{a-3}=\frac{4a-12}{a-3}=\frac{(a-3)+3a-9}{a-3}=\frac{(a-3)+3(a-3)}{a-3}=\frac{(a-3)(1+3)}{a-3}=4\)

Answer (E)
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Re: In the xy-plane, if line k passes through the points (3, -4) and (a,b) [#permalink] New post   05 Sep 2019, 09:57
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Let the eqn. of line k
y = mx + c with slope m.

Since the line k passes through (3, -4) and (a, b) both, we have equations
- 4 = m * 3 + c and b = m * a + c

Subtracting 2nd from 1st gives
- 4 - b = 3m – am
m = (4+b) / (a – 3)

From question b = 4a – 16 and a > 3

If a = 4 then b = 0
 m = 4 + 0 / (4 - 3)
 m = 4

Answer E.
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Re: In the xy-plane, if line k passes through the points (3, -4) and (a,b) [#permalink] New post   05 Sep 2019, 11:26
b-(-4)/a-3 = 4a-16+4/a-3=
4a-12/a-3
As a>3 so, A,B, and C could not be the answer. If we let a, 4 therefore b is 0.(4,0)
0-(-4)/4-3=4/1=4
Option E

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Re: In the xy-plane, if line k passes through the points (3, -4) and (a,b) [#permalink] New post   05 Sep 2019, 15:15
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In the xy-plane, if line k passes through the points (3, -4) and (a, b), where b = 4a - 16 and a > 3 what is the slope of k?

Slope = \(\frac{b-(-4)}{a-3}\)
Let's say a = 4
b = 16-16 = 0
slope = \(\frac{0+4}{4-3}\) = 4

E is the answer!
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Re: In the xy-plane, if line k passes through the points (3, -4) and (a,b) [#permalink] New post   28 Feb 2024, 00:04
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Re: In the xy-plane, if line k passes through the points (3, -4) and (a,b) [#permalink]
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