Question 970218
slope using first two points, (3,7) and (x,2) is (-5)/x-3 ;  we subtract the 7 from the 2 (difference in y) and 3 from x (difference in x). Notice we have an x generic for slope and an algebraic x. 

slope using the first and third points will be equal to the first if we have a line.  That slope is (y-7)/(-3-3) or (y-7)/-6

Set them equal to 5/3 since that is the numerical value of the slope given.

[-5/(x-3)]=5/3
Cross multiply.  -15=5(x-3)
-15=5x-15  by distributing.
add 15 to both sides.
0=5x; x=0

[(y-7)/-6]=5/3
Cross multiply
3(y-7)=(-6)*5)
3y-21=-30
3y=-9, adding 21 to both sides
y=-3, dividing both sides by 3


(3,7)
(0,2)
(-3, -3)  are the points.

Check slope between the points
(3,7) and (0,2);   (2-7))/(0-3) ;   -5/-3  or 5/3
(0,2) and (-3,-3);   (-3-2)/-3 ;   -5/-5 or 5/3

x=0
y=-3

Notice that the points are on the line y=(5/3)x +2


{{{graph(300,300,-5,5,-5,10,(5/3)x+2)}}}