What is the slope and one point on the graph of
y-12=4/9 (x+7)

Ok first lets get the slope like this:
 y -12 = 4/9 (x+7) 

y = 4/9 (x+7) + 12 
y = 4x/9 + 28/9 +12 
y = 4x/9 + 118/9 

Slope is = 4/9
 Now for the point on the graph put x=0 and find y for the point. I hope this is good enough for you