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Re: The slope of the line passing through the point (5,5) is 5/6. All of [#permalink]
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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]
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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]
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