In the xy-plane, if line k passes through the point (-5, a), where a

Question

In the xy-plane, if line k passes through the point (-5, a), where a ≠ -5, is the slope of line k positive ?

(1) Line k passes through the point (a, -5)
(2) The x-intercept of line k is greater than -5

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Rabab36 · Answer

statement 1

line k passes through point (-5,a) and (a,-5)

therefore slope = y2-y1/x2-x1
 = -5-a/a=5

slope = -1

sufficient

Statement II
x intercept is gretaer than -5

points may be (-4,0),(-3,0),(-2,0),(-1,0)
given point (-5,a)

slope=0-a/-4+5

slope= -a/5

depending on value of a
slope can be positive or negative

therefore not sufficient

option A correct

Shashi128 · Answer

Let point A be (-5,a) taking point B (a,-5) given in statement 1 then slope of AB will be a-(-5) / -5-a = -1 .
Now taking statement 2 let C be any point such that it's cordinate is -5+m, 0 when line intercepts x axis where is positive number . Now slope of AC will be a-0/-5-(-5+m)=a/-m we don't know if a is negative or positive so condition can't be determined from statement 2 so A is the answer

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gmatophobia · Answer

Statement 1

Line k passes through the point (a, -5)

We can find the slope of the line if we know the coordinates of two points on the line. Assume that the line passes through  (x_1,y_1)  and  (x_2 , y_2)

Slope =  \frac{y_2 - y_1 }{ x_2 - x_1}

Using this concept, slope of the line =  \frac{a - (-5) }{ -5 - a} 
=  \frac{a + 5 }{ -(5 + a)} 
= -1

The statement is sufficient. Hence we can eliminate option B, C and E.

Statement 2

The x-intercept of line k is greater than -5

Knowing the x intercept would not help as we don't have information on y intercept or any additional information in the premise to get the slope.

Insufficient.

Option A

In the xy-plane, if line k passes through the point (-5, a), where a

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GMAT Data Sufficiency (DS) Questions

In the xy-plane, if line k passes through the point (-5, a), where a

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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Perfect 805 Score Debrief by Julia

My Rewards