Answer:
The slope of the line is 3.
Step-by-step explanation:
Given function;
x(t) = -t² + 5t
y(t) = 3t, when t = 2
[tex]\frac{dx}{dt} = -2t + 5[/tex]
[tex]\frac{dy}{dt} = 3[/tex]
[tex]\frac{dy}{dx}= \frac{dy}{dt} \ \times \ \frac{1}{\frac{dx}{dt} } \\\\\frac{dy}{dx}= 3 \ \times \frac{1}{-2t + 5} \\\\\frac{dy}{dx}= \frac{3}{-2t + 5}[/tex]
t = 2
[tex]Then, \ \frac{dy}{dx}= \frac{3}{-2(2) + 5} \\\\\frac{dy}{dx}= \frac{3}{-4 + 5} \\\\\frac{dy}{dx}= \frac{3}{1} \\\\\frac{dy}{dx}= 3[/tex]
Therefore, the slope of the line is 3.
