Question

Select the correct answer. TBM Use (days) Tunnel Length (feet) 6 410 15 815 20 1,040 28 1,400 33 1,625 38 1,850 45 2,165 During a construction project, engineers used explosives to excavate 140 feet of tunnel into a mountain. But because of time constraints and environmental concerns, they brought in a tunnel boring machine (TBM) to excavate the rest of the tunnel. The data table lists some observations an engineer made about the length of the tunnel after the TBM was introduced. How much of the tunnel was completed 26 days after the TBM was introduced?

Answer 1

X = number of days, y = tunnel completion amount in ft
(6,410)(15,815)
slope = (815 - 410) / (15 - 6) = 405/9 = 45

y = mx + b
slope(m) = 45
(6,410)....x = 6 and y = 410
sub and find b
410 = 45(6) + b
410 = 270 + b
410 - 270 = b
140 = b

equation is : y = 45x + 140

after 26 days....x = 26

y  = 45(26) + 140
y = 1170 + 140
y = 1310 ft <==