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\[y=-17; x _{0}=3\]

so what do you do with the 3

there has to be more to this question which you have not given us

if the equation for y is simply: y = -17 .. then daru is correct.

sorry wrong problem
\[y=6-2x; x_{0}=3\]

both

wouldn't the derivative be 2

almost, that negative sign (subtraction) needs to be recognized :)
y= 6 - 2x
y' = 6' - (2x)'
= 0 - 2

oh ok.

/so how do you find that slope of tangent after taking the derivative?

the value of the derivative DEFINES the slope of the tangent at a given point.

in this case, 6 - 2x is a straight line whose sloe is -2 at all points

so in a problem such as f(x)=5x-3
the slope of the line that is tangent is 5?

yes

ok. thanks