Bunuel wrote:

In the xy-plane, line l passes through the point (-7, k). What is the value of the y-intercept of line l ?

(1) The x-intercept of line l is 4.

(2) Line l and line n are parallel and the equation of line n is y=x+5

Kudos for a correct solution.

Answer : C

My approach:

let the equation of the line be y =mx+c, where m is the slope and c is the constant.

from stem, line passes through (-7,k). This is a point on the line.

k=-7m+c ------> (1)

from 1: x intercept is 4, so (4,0) is a point on the line

4m + c = 0 ---> (2)

solving 1 and 2 for m and c in terms of k we have: m = k/11 and c = -4k/11

equation of the line is then y = kx/11-4k/11

y intercept is when x = 0 => y intercept = -4k/11, as k can be any value --> not sufficient

from 2: line is parallel to y = x+5, so slope of the line is 1. equation of the line reduces to

y = x+c. (c = k+7, from stem as m = 1).

y -intercept = c = k+7 : NSF

from 1+2 combined

(4,0) is a point on the line from 2, y= x+k+7 => k = -11. From this y - intercept = -4*-11/11= 4. sufficient