Thread: Lines in a Plane 9

For each of the following lines, state a direction vector with integer components. If possible, name a point on the line with integer coordinates.

a) x=1/3 + 2t
y=3 - 2t/3

so this is my attempt, but I am not sure what I did wrong and how to get the correct answer.

d=(2, -2/3)
P=(1/3, 3)

But now to find integer values of the above..
d=(3,-1)
P=(1,9)

But in the back of the book, the answer is
d=(3,-1) << which I have, BUT they do not have a possible point on the line.. does it mean that there are no other integer values on the line, or is there answer wrong?

Originally Posted by skeske1234

a) x=1/3 + 2t
y=3 - 2t/3
d=(2, -2/3)
P=(1/3, 3)

But now to find integer values of the above..
d=(3,-1)
But in the back of the book, the answer is
d=(3,-1) << which I have, BUT they do not have a possible point on the line.. does it mean that there are no other integer values on the line?

If we write the equation is this form, , then when will a multiple if three be 28?
Ever?