Thank you for the opportunity to help you with your question!

y=(-2/3)x+1

Parallel lines in a set of plane have the same slope. Therefore a line parallel to this(above equation) has a slope of -2/3

To get the set of points we get a random value of x say x=3 and we find

the value of y using the equation above

y=(-2/3)*3+1

y=-2+1

y=1

Therefore one point is (3,1)

To get another point take another value of x randomly as 9

Therefore

y=(-2/3*9)+1

y=-6+1

y=5

The other point is (9,5)

The points of a line parallel to y=(-2/3)x+1 are

(3,1),(9,5)

To get more points you use the same method.

Please let me know if you need any clarification. I'm always happy to answer your questions.

Oct 7th, 2015

Sorry Resell the answer i gave you previously has some wrong value! The values of y are -1 and -5 respectively, I just miscalculated the values! The points should be (3,-1) and (9,-5) respectively.