What is the slope of #f(t) = (t-1,t+3)# at #t =1#?

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Answer 1 · 2016-02-16T23:37:56

#1#

The derivative of the parametric function

#f(t)=(x(t),y(t))#

is

#f'(t)=(x'(t))/(y'(t))#

The given parametric function is

#f(t)=(t-1,t+3)#

which means that

#x(t)=t-1#
#y(t)=t+3#

Differentiation of both functions with respect to #t# yields

#x'(t)=1#
#y'(t)=1#

so the entire parametric function's derivative is

#f'(t)=(x'(t))/(y'(t))=1/1=1#

This means that, irrespective of the value of #t#, the slope of the tangent line to the function is always #1#.