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by trangle » Sat Jan 15, 2011 8:16 pm
The y-intercept of a line l is 4. If the slope of l is negative, which of the following could be the x-intercept of l?
I. -1
II. 0
III. 6

a. I only
b. II only
c. III only
d. I, II, and III
e. I and II only

OA: b
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by Anurag@Gurome » Sat Jan 15, 2011 8:41 pm
trangle wrote:The y-intercept of a line l is 4. If the slope of l is negative, which of the following could be the x-intercept of l?
I. -1
II. 0
III. 6

a. I only
b. II only
c. III only
d. I, II, and III
e. I and II only
Say the equation of l is y = mx + c
Where m is the slope and c is the y-intercept.

Now, x-intercept of the line is the value of x, when y is zero.
=> x-intercept = -(c/m)

According to the question, c = 4 and m < 0.
Hence, x-intercept = -(c/m) = -(4/m) = Some positive quantity as m < 0.

Possible value of x-intercept is 6.

The correct answer is C.

Note: Check the OA again. If x-intercept of the line is zero, then the line can never have a negative slope. Then it'll be perpendicular to x-axis, i.e. of infinite slope.
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by pesfunk » Thu Jan 27, 2011 6:57 am
Even my answer comes to C. It must be the right answer.
Anurag@Gurome wrote:
trangle wrote:The y-intercept of a line l is 4. If the slope of l is negative, which of the following could be the x-intercept of l?
I. -1
II. 0
III. 6

a. I only
b. II only
c. III only
d. I, II, and III
e. I and II only
Say the equation of l is y = mx + c
Where m is the slope and c is the y-intercept.

Now, x-intercept of the line is the value of x, when y is zero.
=> x-intercept = -(c/m)

According to the question, c = 4 and m < 0.
Hence, x-intercept = -(c/m) = -(4/m) = Some positive quantity as m < 0.

Possible value of x-intercept is 6.

The correct answer is C.

Note: Check the OA again. If x-intercept of the line is zero, then the line can never have a negative slope. Then it'll be perpendicular to x-axis, i.e. of infinite slope.
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