Question

Find the slope of a line having a parametric equation of x = 2 + t and y = 5 - 3t

• A. 2
• B. 3
• C. -2
• D. -3

Answer 1

The correct option is D -3

Given,

$x=2+t$

$y=5-3t$

Slope of line i given by $\frac{dy}{dx}$

Now,

$\frac{dx}{dt}=\frac{d}{dt}(2+t)$

$=\frac{d}{dt}\left(2\right)+\frac{d}{dt}\left(t\right)$

$=0+1$

$=1$

And,

$\frac{dy}{dt}=\frac{d}{dt}(5-3t)$

$=\frac{d}{dt}\left(5\right)-\frac{d}{dt}\left(3t\right)$

$=0-3$

$=-3$

$\therefore \frac{dy}{dx}=\frac{\frac{dy}{dt}}{\frac{dx}{dt}}$

$=\frac{-3}{1}$

$=-3$