Question

State the coordinates of two points on the following line

x=3-8t
y=4t

For one point I got (3,0). In the back of the book it says (11, -4) for another point. How would I get that?

b) r = (4,0) + t(0, 5)
I got (4,0) for one point. In the back of the book it says (4,10) for another point. How would I get that?

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State a direction vector with integer components.

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

State the integer components and name a point on the line with integer coordinates.

r = (1/3, 1/2) + t(1/3, 1/4)

Answer 1

x=3-8t
y=4t

let t=-1


b) for r = (4,0) + t(0, 5)

let t=2
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x = (1/3) + 2t, y = 3-(2/3)t
so r= (1/3,3) + t(2,2/3)

a direction vector is
(2,2/3) or (4,2) or (8,4), or ....

do you follow?

for the last one, what do you think should be value of t to have integer solutions?