there is a straight line 2x+y=10 on the Cartesian plane. how do I turn it into the vector form of [1 -2]?

Answer 1

To transform the equation of the straight line 2x + y = 10 into vector form, we can rewrite it as a system of equations:

2x + y = 10

By rearranging the equation, we isolate y:

y = 10 - 2x

Now, we can rewrite the equation in vector form by setting x = t (a parameter) and expressing y in terms of t:

y = 10 - 2t

Finally, we represent the line in vector form as:

[r(t)] = [t, 10 − 2t] = [1, -2]t

Therefore, the vector form of the given straight line is [1, -2].