1. ## Parametric Equations

x = -4 + 3t
y = 1 + 2t
The displayed equations are called
parametric, and t is called a parameter. How is the slope of a line determined from its parametric equations?

* I already know I can find the slope by plugging in values for t and plotting the points or using the slope formula...

2. $m = \dfrac{\Delta y}{\Delta x} = \dfrac{y(t_2) - y(t_1)}{x(t^2) - x(t_1)} = \dfrac{(1+2t_2)-(1+2t_1)}{(-4+3t_2)-(-4+3t_1)} = \dfrac{2(t_2-t_1)}{3(t_2-t_1)} = \dfrac{2}{3}$

in short, note that slope of the line is equal to the rate of change of y divided by the rate of change of x