The tangent value of the angle between the x-axis and the line, directed by the vector, -2j-9i,is:?

Question

(a) 9/2 (b) –2/9 (c) 2/9 (d) ∞

Answer 1

the line is just a function 2y=9x

therefore y = (9/2)x, and the tangent is just the derivative of the function, which is simply:

dy/dx = 9/2

so the answer is (a)

Answer 2

Let
m = slope line

m = ∆y/∆x = -2/-9 = 2/9
m = tanθ = 2/9

Note that the y value is given first in the expression.