Parametric Equations

Question

Parametric equations for the line segment between (-2,10) and (7,2) have the form:

x(t)=a+bt

y(t)=c+dt

If the parametric curve starts at (-2,10) when t=0 and ends at (7,2) at t=1, then find a, b, c, and d.

Answer 1

ok so a is your x-value at t=0, you can think of it as the x-intercept if you graphed just the x(t) function. the c value is the same but for y(t). Therefore:

a=-2 (what x equals when t is zero)

c=10 (what y equals when t is zero)

then you have to find b and d. They are the slopes of x and y with respect of time so instead of doing change in y over change in x, you do Δx/Δt for b and Δy/Δt for d

b=(7-(-2))/(1-0)=9/1=9

d=(2-10)/(1-0)=-8/1=-8

so x(t)=-2+9t and y(t)=10-8t