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Which of the following could be the slope of a line that passes throug

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Bunuel
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Which of the following could be the slope of a line that passes throug [#permalink] New post   02 Jul 2020, 03:01
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Which of the following could be the slope of a line that passes through the point (–2, –3) and crosses the y-axis above the origin?

I. \(\frac{5}{3}\)

II. \(\frac{9}{4}\)

III. \(4\)


(A) I only
(B) III only
(C) I and II only
(D) I and III only
(E) I, II, and III
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E
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rajatchopra1994
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Re: Which of the following could be the slope of a line that passes throug [#permalink] New post   02 Jul 2020, 03:09
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Explanation:

If line passes through the origin (0,0) then the slope is 3/2.
The line should pass above the origin, which means slope should be greater than 3/2.

Option 1,2,3 all are greater than 3/2

IMO-E
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Re: Which of the following could be the slope of a line that passes throug [#permalink] New post   02 Jul 2020, 03:58
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Bunuel wrote:
Which of the following could be the slope of a line that passes through the point (–2, –3) and crosses the y-axis above the origin?

I. \(\frac{5}{3}\)

II. \(\frac{9}{4}\)

III. \(4\)


(A) I only
(B) III only
(C) I and II only
(D) I and III only
(E) I, II, and III


A line that passes through (–2, –3) and origin will have slope = 3/2 as depicted by red line in attachment

A line that passes through (–2, –3) and above origin will have slope > 3/2 as depicted by Blue line in attachment

therefore \(Slope > \frac{3}{2}\)

I. \(\frac{5}{3}\)

II. \(\frac{9}{4}\)

III. \(4\)

All values are greater than 3/2 hence

Answer: Option E
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Re: Which of the following could be the slope of a line that passes throug [#permalink] New post   02 Jul 2020, 03:58
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Bunuel wrote:
Which of the following could be the slope of a line that passes through the point (–2, –3) and crosses the y-axis above the origin?

I. \(\frac{5}{3}\)

II. \(\frac{9}{4}\)

III. \(4\)


(A) I only
(B) III only
(C) I and II only
(D) I and III only
(E) I, II, and III


    Solution
    • Let’s say the line which passes through the point (-2, -3) and crosses the y – axis above the origin is y= mx + c,
      o Where m and c are slope and y intercept of the line, respectively.
    • Substituting the point (-2, -3) in the equation of the line we, get,
      o \(-3 = -2m +c\)
      \(⟹ c = 2m – 3\)
    • Since, line crosses y- axis above origin,
      o So, \(c > 0\).
        \(⟹ 2m – 3 > 0\) \(⟹ m > \frac{3}{2}\)
    • Now, let’s check which value/s amongst the given statements is/are greater than \( \frac{3}{2} \) or \(1.5\)

Statement I
    • \(\frac{5}{3} = 1. 667\)
      o So, \(\frac{5}{3} > \frac{3}{2} \)
    • Hence, \(\frac{5}{3} \) could be the slope of the given line.

Statement II
    • \(\frac{9}{4} > 2 > \frac{3}{2} \)
    • Hence, \(\frac{9}{4} \) could be the slope of the given line.

Statement III
    • \( 4 > \frac{3}{2} \)
    • Hence, \( 4 \) could be the slope of the given line.

Thus, the correct answer is Option E.
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Re: Which of the following could be the slope of a line that passes throug [#permalink] New post   02 Jul 2020, 06:01
I have a different approach to this question
given that eq of line is y=mx+c where c>0
we put the values of m to check whether the c>0 for what values.
gladly all three satisfies
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Re: Which of the following could be the slope of a line that passes throug [#permalink] New post   15 Sep 2021, 11:51
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Re: Which of the following could be the slope of a line that passes throug [#permalink]
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