Find Length of r(t) on [0,3]: Sketching the Plane Curve in xy-Plane

[p4nda]

Sketch the plane curve in the xy-plane and find its length over the given interval:
r(t) = (6t-3)i + (8t+1)j on [0,3]

Here's what I've got so far:
r'(t) = 6i + 8j
llr'(t)ll = sqrt of 6^2+8^2 = 10
s = integral 0-3 10dt
= 10x ]0 to 3
= [30-0]
= 30I just need help on how to sketch this plane curve. Thanks.

 

[quasar987]

to sketch curves, you can only find the derivative to get an idea of how the curve behave and then just calculate a bunch of points and link them together. it's tedious and boring, just hang on.

 

[HallsofIvy]

Since the functions for the x and y components are linear, this is, of course, a straight line! Find the point corresponding to t= 0, the point correponding to t= 3 and draw the straight line between them.