Answer:
[tex]\frac{dy}{dx}=-2[/tex]
Step-by-step explanation:
Given a set of parametric equations that represent a line. Find the slope of the line without eliminating the parameter.
[tex]x = 7 + 2t \\ y = 5 - 4t[/tex]
Differentiate each equation with respect to t.
[tex]x = 7 + 2t \\\\\Longrightarrow \boxed{ \frac{dx}{dt}=2}[/tex]
[tex]y = 5-4t \\\\\Longrightarrow \boxed{ \frac{dy}{dt}=-4}[/tex]
[tex]\boxed{\left\begin{array}{ccc}\text{\underline{Note:}}\\\\\Big{\frac{dy}{dx}=\frac{(\frac{dy}{dt} )}{(\frac{dx}{dt})}} \end{array}\right}[/tex]
[tex]\frac{dy}{dx}=\frac{(\frac{dy}{dt} )}{(\frac{dx}{dt})}} \\\\\Longrightarrow \frac{dy}{dx}=\frac{-4}{2} \\\\\therefore \boxed{\boxed{\frac{dy}{dx}==-2}}[/tex]
Thus, the problem is solved.
