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.

Which equation represents the length of the completed tunnel based on the number of days since TBM was introduced?

Question

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.

Which equation represents the length of the completed tunnel based on the number of days since TBM was introduced?

Mercury · Answer

this is a linear function, so you can simply pick any two points for the equation

I would recommend 
(6, 410)
(15, 815)
since these are the smallest values

plug these into the slope formula
once you have the slope, take y = mx + b, pick a point, plug in x, y, and m, then solve for b

then re-write the whole equation, with m and b