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Line J has a y-intercept of 6 and passes through point (a,b). What is

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Bunuel
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Line J has a y-intercept of 6 and passes through point (a,b). What is [#permalink] New post   11 Oct 2015, 09:28
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Line J has a y-intercept of 6 and passes through point (a,b). What is the slope of Line J in terms of a and b?

A. (a−6)/b
B. (a−b)/6
C. (6−a)/b
D. (6−b)/a
E. (b−6)/a

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E
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riteshgmat
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Re: Line J has a y-intercept of 6 and passes through point (a,b). What is [#permalink] New post   16 Oct 2015, 22:56
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Just another alternate way.

Equation of line :

y = mx + b, where b is the y-intercept & m is the slope.

We have given y-intercept of this line as 6 and the line passes through point(a,b).

Therefore,

b = ma + 6

ma = ( b - 6 )

m = \(\frac{( b - 6 )}{a}\)


Answer is E
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Line J has a y-intercept of 6 and passes through point (a,b). What is [#permalink] New post   11 Oct 2015, 11:02
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Bunuel wrote:
Line J has a y-intercept of 6 and passes through point (a,b). What is the slope of Line J in terms of a and b?

A. (a−6)/b
B. (a−b)/6
C. (6−a)/b
D. (6−b)/a
E. (b−6)/a

Kudos for a correct solution.


Given points (0,6) and (a,b) Slope=\(\frac{6-b}{0-a}\) = \(\frac{b-6}{a}\) Answer (E)
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Re: Line J has a y-intercept of 6 and passes through point (a,b). What is [#permalink] New post   11 Oct 2015, 11:09
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Here the points are given as (a,b) and (0,6) because the y intercept is 6 and hence x will be 0.

Putting m = y2-y1/x2-x1 we would get b-6/a-0 => (b-6)/a

Answer E
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Re: Line J has a y-intercept of 6 and passes through point (a,b). What is [#permalink] New post   11 Oct 2015, 21:58
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Bunuel wrote:
Line J has a y-intercept of 6 and passes through point (a,b). What is the slope of Line J in terms of a and b?

A. (a−6)/b
B. (a−b)/6
C. (6−a)/b
D. (6−b)/a
E. (b−6)/a

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The two points given here are (0,6) and (a,b)

Slope m =b-6/a

Answer: E
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Bunuel
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Re: Line J has a y-intercept of 6 and passes through point (a,b). What is [#permalink] New post   18 Oct 2015, 12:18
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Bunuel wrote:
Line J has a y-intercept of 6 and passes through point (a,b). What is the slope of Line J in terms of a and b?

A. (a−6)/b
B. (a−b)/6
C. (6−a)/b
D. (6−b)/a
E. (b−6)/a

Kudos for a correct solution.


VERITAS PREP OFFICIAL SOLUTION:

You know that the line goes through point (a,b) and the y-intercept of 6 tells you that the line also goes through point (0,6). So you can use the "rise over run" slope formula to calculate the slope. Recognizing that the five answer choices focus on a,b, and 6, you should see that you should subtract 0 and 6 (subtracting 0 is the same as doing nothing at all) to get your math looking like the answer choices. So you'll set up the equation:

(b−6)/(a−0), and end up with answer choice E.
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Line J has a y-intercept of 6 and passes through point (a,b). What is [#permalink] New post   14 Jul 2016, 08:10
Bunuel wrote:
Line J has a y-intercept of 6 and passes through point (a,b). What is the slope of Line J in terms of a and b?

A. (a−6)/b
B. (a−b)/6
C. (6−a)/b
D. (6−b)/a
E. (b−6)/a

Kudos for a correct solution.


when x = 0 then y= 6
when x = a then y=b

\(slope =\frac{y2-y1}{x2-x1}\)

\(slope =\frac{6-b}{a-0}\)

\(slope =\frac{6-b}{a}\)

Answer is E
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Re: Line J has a y-intercept of 6 and passes through point (a,b). What is [#permalink] New post   17 Jan 2022, 11:45
y-intercept is 6, therefore the line passes through the point (0,6). Also, given that the line also passes through point (a,b) therefore the slope of the line is (y2-y1)/(x2-x1)=(b-6)/a. Hence, option E
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Re: Line J has a y-intercept of 6 and passes through point (a,b). What is [#permalink]
17 Jan 2022, 11:45
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