# Thread: Is the point on the line?

1. ## Is the point on the line?

Determine if each point P is on the line [x,y] = [2,-3] + t[4,7]
a) P(-2,-10)
b) P(6,5)
c) p(10,14)
d) P(4, 0.5)

We just learned this today and I'm not sure of the difference between vector r and vector "r not" from r = r0 + tm. I'm not sure where to substitute the given points.

2. Originally Posted by TN17
Determine if each point P is on the line [x,y] = [2,-3] + t[4,7]
a) P(-2,-10)
b) P(6,5)
c) p(10,14)
d) P(4, 0.5)
To be absolutely clear, you need to give a value for $\displaystyle t$ in every yes answer.

3. Originally Posted by TN17
Determine if each point P is on the line [x,y] = [2,-3] + t[4,7]
a) P(-2,-10)
b) P(6,5)
c) p(10,14)
d) P(4, 0.5)

We just learned this today and I'm not sure of the difference between vector r and vector "r not" from r = r0 + tm. I'm not sure where to substitute the given points.
$\displaystyle x = 2+4t$ solve for t in terms of x ...

$\displaystyle t = \dfrac{x-2}{4}$

$\displaystyle y = -3+7t$

substitute for t ...

$\displaystyle y = -3 + 7 \cdot \dfrac{x-2}{4}$

now check the points ...