Question

given each scalar equation, write a vector equation and the parametric equation. a) x+2y=6

Answer 1

Can you tell me the normal vector of this line?

Answer 2

thats all im given

Answer 3

Yes, I see that :-) Do you know about the normal vector yet? Or haven't you covered that topic? Because the normal vector, is the vector that can be read very easily from the equation above.

Answer 4

oh so it would be [1,2]

Answer 5

is that right?

Answer 6

exactly, now that is a normal vector of the line, you need to compute the direction vector
HINT: The Dot Product has to be equal to zero.

Answer 7

ok so the slope would be [-2,1]

Answer 8

right?

Answer 9

Well, you do not call that precisely the slope in parametric form, but that is the direction vector you can use for the curve.

Now you only need to find a point that is on the line, can be any point.

Answer 10

um how do i find that

Answer 11

But you're right, you computed it right, I just call it a direction vector, because that's what it is - but it does indeed correlate to the slope of the function too, I am just being careful with the terminology here.

Finding a point on a line is very easy. You just plugin values that satisfy the equation. For instance (0,0) Is that point on the graph?

\[0+2\cdot0\neq6 \]
No it's clearly not on the graph.

Answer 12

ohh ok so the points have to equal to 6

Answer 13

[2,2]?

Answer 14

for instance yes

Answer 15

can be any point, could be (0,3) too

Answer 16

but that's not important, it's up to you which one you choose.

Answer 17

ok and what do i do after that

Answer 18

For the vector equation you just plug it all in, so it will look like that: