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The slope of the line passing through the point (5,5) is 5/6. All of

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Bunuel
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The slope of the line passing through the point (5,5) is 5/6. All of [#permalink] New post   16 May 2016, 02:43
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The slope of the line passing through the point (5,5) is 5/6. All of the following points could be on the line except

A. (2.5, 2)
B. (11, 10)
C. (8, 7.5)
D. (-1, 0)
E. (-7, -5)

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The slope of the line passing through the point (5,5) is 5/6. All of [#permalink] New post   16 May 2016, 04:51
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Bunuel wrote:

The slope of the line passing through the point (5,5) is 5/6. All of the following points could be on the line except

A. (2.5, 2)
B. (11, 10)
C. (8, 7.5)
D. (-1, 0)
E. (-7, -5)

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Attachment:
p005-6.gif


Hi,
SLOPE = \(\frac{(y_2 - y_1)}{(x_2 - x_1)} = \frac{5}{6}\)...

one set of coord is (5,5) and other is given in the choices, so lets test the choices


A. (2.5, 2) .......... \(\frac{5-2}{5-2.5}= \frac{3}{2.5} = \frac{6}{5}\neq{\frac{5}{6}}\)... ANSWER
B. (11, 10) .......... \(\frac{5-10}{5-11}= \frac{-5}{-6} = \frac{5}{6}={\frac{5}{6}}\)
C. (8, 7.5) .......... \(\frac{5-7.5}{5-8}= \frac{-2.5}{-3} = \frac{5}{6}={\frac{5}{6}}\)
D. (-1, 0) .......... \(\frac{5-0}{5-(-1)}= \frac{5}{6} = \frac{5}{6}={\frac{5}{6}}\)
E. (-7, -5) .......... \(\frac{5-(-5)}{5-(-7)}= \frac{10}{12} = \frac{5}{6}={\frac{5}{6}}\)

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Re: The slope of the line passing through the point (5,5) is 5/6. All of [#permalink] New post   16 May 2016, 03:27
The slope-point form of equation with point (a,b) and slope m : (y - a) = m(x - a)

Thus for this particular graph, our equation is
(y - 5) = 5/6 * (x - 5)
On rearranging,
-5x + 6y = 5

Now, we can check which of the options doesn't agree with the above equation

Option A. (2.5, 2) doesn't satisfies the equation
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Re: The slope of the line passing through the point (5,5) is 5/6. All of [#permalink] New post   29 Sep 2019, 05:32
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Solution



Given

• Slope of a line is 5/6.
• It passes through (5, 5)

To find
• The line cannot pass through which point.

Approach and Working out

We have information only about the slope. So, we will apply the formula of that.
• m = (y2- y1)/(x2- x1)

m is 5/6. Let’s take (x2, y2) = (5, 6) and (x1, y1) = (x, y).
• (x, y) are the points from which the line can pass.
• 5/6 = (5- y)/ (5 - x)
• 25 - 5x = 30 – 6y
• 6y – 5x = 5
• y+ 5y – 5x= y + 5(y-x) = 5

Let check all the options.

Option A: (2.5, 2)
• 2 + 5(2 – 2.5) = 2 + 5* - 0.5 =2 – 2.5 =-0.5 ≠ 5 -> Answer

Option B: (11, 10)
• 10 +5(10- 11) = 5

Option C: (8, 7.5)
• 7.5 + 6(7.5 -8) = 5

Option D: (-1, 0)
• 0+5(0- (-1) ) = 5

Option E: (-7, -5)
• -5 + 5(-5 +7) = 5
Hence, option A is the correct answer.

Correct Answer: Option A
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Re: The slope of the line passing through the point (5,5) is 5/6. All of [#permalink] New post   30 Apr 2023, 21:03
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Given: The slope of the line passing through the point (5,5) is 5/6.
Asked: All of the following points could be on the line except

y = mx + c
where m is the slope of the line

y = 5x/6 + c

Since the line passes through the point (5,5)
5 = 5*5/6 + c
c = 5/6

Equation of the line
y = 5x/6 + 5/6
6y = 5x + 5

A. (2.5, 2) : 6y=12; 5x + 5 = 5*2.5 + 5 = 12.5+5 = 17.5: Incorrect
B. (11, 10) : 6y=60; 5x + 5 = 5*11 + 5 = 55+5 = 60: Correct
C. (8, 7.5) : 6y=45; 5x + 5 = 5*8 + 5 = 40+5 = 45: Correct
D. (-1, 0) : 6y=0; 5x + 5 = 5*(-1) + 5 = -5+5 = 0: Correct
E. (-7, -5) : 6y=-30; 5x + 5 = 5*(-7) + 5 = -35+5 = -30: Correct

IMO A
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Re: The slope of the line passing through the point (5,5) is 5/6. All of [#permalink]
30 Apr 2023, 21:03
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