Line k lies in the xy-plane. The x-intercept of line k is -4, and line

Question

Line k lies in the xy-plane. The x-intercept of line k is -4, and line k passes through the midpoint of the line segment whose endpoints are (2, 9), and (2, 0). What is the slope of line k ?

A. 1/8
B. 1/4
C. 1/2
D. 3/4
E. 7/8

Archit3110 · Answer

good question..

plot on graph the values for (2,9) & (2,0) ; the mid point of this line would be (2,4.5) which would be the point of intersection of the line k
slope of line k : ( 4.5-0)/(2+4) = 4.5/6 ~ 3/4 IMO D

sunita123 · Answer

can we calculate slope from equation y =mx+c?
4.5= m*2-4 (here -4 is x intercept)
then m =8.5/2=17/4 , what is wring here?

Archit3110 · Answer

sunita123 
In a linear equation y= mx + c 
: m is the slope of the line. c is the value of the intercept on the y-axis.

-4 is the x intercept not y..

Hope this helps..

sunita123 · Answer

Ah , my bad , that is Y intercept . Thank you very much Archit3110.

Srikantchamarthi · Answer

Archit3110  is it the slope or the midpoint of line k ? y2-y1/x2-x1

Archit3110 · Answer

Srikantchamarthi

slope m = y2-y1/x2-x1

mid point= x1+x2/2 , y1+y2/2

fauji · Answer

Approach:

From Given data: 
- We can get midpoint of line segment whose endpoints are (2, 9), and (2, 0) ---> MidPoint (x2,y2) is (2, 4.5)
- The x-intercept of line k is -4 (means y =0) --> this point be (x1,y1) = (-4,0)

- Now, We have 2 endpoints for a line segment, we can find slope by equation:

\frac{ y-y1}{x-x1}  =  \frac{y1-y2}{x1-x2}

\frac{ y-0}{x+4}  =  \frac{0-4.5}{-4-2}

y  =  \frac{-4.5x}{-6} + 4

Slope =  \frac{4.5}{6}  = ~ \frac{3}{4}

Option D

JoeJoeGRE2026 · Answer

Hello,

I rarely post on this forum. It may even be my first time, so my apologies if I'm not following proper protocol.

I am confused. I get where 4.5 is the midpoint for y, but why is the midpoint for x = 2 and not x = 1, since y (4.5) is half of 9?

Thanks in advance!

Bunuel · Answer

For endpoints (x1, y1) and (x2, y2), the midpoint is ((x1 + x2)/2, (y1 + y2)/2), meaning you average the x coordinates and average the y coordinates.

Here the endpoints are (2, 9) and (2, 0), so the midpoint is ((2 + 2)/2, (9 + 0)/2) = (2, 4.5). That is why the midpoint x is 2, not 1.

JoeJoeGRE2026 · Answer

Thanks for the response! I'll check my answer with your new information.

Line k lies in the xy-plane. The x-intercept of line k is -4, and line

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Line k lies in the xy-plane. The x-intercept of line k is -4, and line

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