The endpoints of jk are j(–25, 10) and k(5, –20). what is the y-coordinate of point l, which divides jk into a 7: 3 ratio

We are looking the coordinate that divides that segment into a 7/3 ratio.  If we are dividing that segment and looking for a particular coordinate, we must first divide the segment into 7+3 segmments, or 10 equal length segments.  When we plot point L on the segment in a 7/3 ratio, notice that L is 7/10 of the way from J to K.  That ratio is k, found by writing the numerator of our ratio over the sum of the numerator and denominator.  Our k then is 7 over 7+3, so k = 7/10.  Now we will find the rise and the run (aka the slope) of the line.  .  We have a rise value of -30 and a run value of 30.  The point L's coordinate are found in this formula: .  x1 and y1 are found in the first coordinate, point J (-25, 10).  Filling in accordingly, we have which simplifies to .  Those coordinates then of L are (-4, -11)