Question

N Example 3, the points are(0,3500) and (5,1750). Write an equation that represents the distance y (in feet) remaining after x months. How much time does it take to complete the tunnel?

Answer 1

The time needed is 10 months.

Explanation:

The given points are (0, 3500) and (5, 1750).

First, we use the formula below to find the slope of the line

`m=(y_(2)-y_(1) )/(x_(2) -x_(1) )=(1750-3500)/(5-0)=(-1750)/(5)=-350`

Which means the function is deacrasing with a ratio of 350 feet per month.

Now, we use the slope and one point to find the equation

`y-y_(1) =m(x-x_(1) )\\y-1750=-350(x-5)\\y=-350x+1750+1750\\y=-350x+3500`

This linear function shows that the situation started at the y-intecept (0, 3500), which means the month 0 had already 3500 feet. In other words, the total distance is 3500 feet. Now, the x-intercept will tell us the time needed to travel that distance.

`0=-350x+3500\\-3500=-350x\\x=(-3500)/(-350)\\ x=10`

Therefore, the time needed is 10 months.