Question 1078045
{{{graph(300,300,-10,10,-10,10,-x+7)}}}
The line AB is between (3,4) and (7,0).  It's length is sqrt ((0-4)^2+(7-3)^2)) or sqrt (32)=4 sqrt (2).
P is the location of the point, and it is 1/4 of the way from A to B. (1/4)*4 sqrt(2)=sqrt(2).
The distance formula is the sqrt of the x^2 and y^2 distances 
Therefore, to get sqrt (2), either x or y has to be [sqrt (2)]^2 and the other 0, OR, each has to be sqrt [(1^2) +(1^2)]=sqrt (2).
Since P is on the line, we need to move from A 1 unit towards B in each of the x and y coordinates.  That would make P at (3+1, 4-1) or (4,3).
The line has slope -1, and that is another way of saying the x and y components that make up a slope of -1 are where one is positive 1 and the other -1.