A bug moves linearly with constant speed across my graph paper.

Question

A bug moves linearly with constant speed across my graph paper. I first notice the bug when it is at (3, 4). It reaches (9, 8) after two seconds and (15, 12) after four seconds. (a) Predict the position of the bug after six seconds; after nine seconds; after t seconds. (b) Is there a time when the bug is equidistant from the x- and y-axes? If so, where is it?

Answer 1

t=-1 (0,2)

t=0, (3,4)

t=1 (6,6)

t=2 (9,8)

t=4 (15,12)

t=6 (21, 16)

t=9 (30, 22)

each second x increases by 3, and y increases by 2

graphically the points are on a straight line with slope = 2/3 and intercept = 2

y = (2/3)x + 2

set x=y

x=y= 2x/3 +2

x/3 = 2

x =6= y

(6,6) is the point where the bug is at equal coordinates

after t seconds the position is (3t +3, 2t+4)