# What is the slope of f(t) = (t-2,2t) at t =-1?

Jun 1, 2017

2

#### Explanation:

Slope equals $\frac{\mathrm{dy}}{\mathrm{dx}} = \left(\mathrm{dy} \text{/"dt)/(dx"/} \mathrm{dt}\right)$

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

$\frac{\mathrm{dx}}{\mathrm{dt}} = \frac{d}{\mathrm{dt}} \left(t - 2\right) = 1$

$\therefore \frac{\mathrm{dy}}{\mathrm{dx}} = \frac{2}{1} = 2$

This means that no matter what $t$ is, the slope of the curve at time $t$ will always be 2.

So dy/dx]_(t=1) = 2