Question

Find an interval of t-values such that c(t)=(2t+1,4t-5) parametrizes the segment from (0,-7) to (7,7). What do you do???

Answer 1

for the first point (0,-7)
2t+1 = 0 and 4t-5=7
t = -1/2 for both, that's good

for the point (7,7)
2t+1 = 7 and 4t-5=7
t = 3 for both

so the t-value interval is from t = -1/2 to t = 3

How does one "parametrize" ??