Question

~PLEASE HELP ASAP OFFERING 10 POINTS~

During a construction project, engineers used explosives to excavate 1400 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?

A) 1,170 feet

B) 1,310 feet

C) 1,260 feet

D) 1,400 feet

Answer 1

So this is going to be a linear equation, you can tell by seeing the growth being the same between days 15 and 20 & 33 and 38. We will be using the format, where m = slope and b = y-intercept.

The equation to solve for the slope is . You can use any two ordered pairs on this list. I'll be using 15 and 20.

45 is the slope.

To solve for the y-intercept, plug in 45 in the m variable and any ordered pair into the x and y variable spot. For this, I'll be using (15, 815)

Now putting the equation together () we can plug in 26 into the x variable and solve.

In short, the answer is B. 1,310 feet.

Explanation:

Answer 2

So this is going to be a linear equation, you can tell by seeing the growth being the same between days 15 and 20 & 33 and 38. We will be using the
`y=mx+b` format, where m = slope and b = y-intercept.



The equation to solve for the slope is
`(y_2-y_1)/(x_2-x_1)` . You can use any two ordered pairs on this list. I'll be using 15 and 20.


`(1040-815)/(20-15)= (225)/(5) =45`

45 is the slope.


To solve for the y-intercept, plug in 45 in the m variable and any ordered pair into the x and y variable spot. For this, I'll be using (15, 815)


`815=45(15)+b \\ 815=675+b \\ 140=b`


Now putting the equation together (
`y=45x+140`) we can plug in 26 into the x variable and solve.



`y=45(26)+140 \\ y=1170+140 \\ y=1310`


In short, the answer is B. 1,310 feet.