Question

The amount of fresh water left in the tanks of a nineteenth-century clipper ship is a linear function of the time since the ship left port, as shown in the table. Write an equation in point-slope form that represents the function. Then find the amount of water that will be left in the ship's tanks 60 days after leaving port.

Time (days) Amount (gal)
1 3555
8 3240
15 2925

Answer 1

The equation in point-slope form representing the function of the amount of fresh water left on a clipper ship over time is y - 3240 = -45(x - 8). Upon substituting 60 days for x into the equation, it is determined that there will be 900 gallons of water left in the ship's tanks after 60 days.

Step-by-step explanation:

To write an equation in point-slope form for the linear function that represents the amount of freshwater left in the tanks of the nineteenth-century clipper ship, we first need to calculate the slope of the line. The slope can be found by taking the difference in the y-values (amount of water) and dividing by the difference in the x-values (time).

Using the points in the table (8 days, 3240 gallons) and (15 days, 2925 gallons):

Slope (m) = (2925 - 3240) / (15 - 8)

= (-315) / (7)

= -45 gallons/day

Now, taking one point on the line, for example, (8 days, 3240 gallons), the equation in point-slope form is:

y - 3240 = -45(x - 8)

To find the amount of water left after 60 days, substitute x = 60 into the equation:

y - 3240 = -45(60 - 8)

y - 3240 = -45(52)

y - 3240 = -2340

y = 3240 - 2340

y = 900 gallons

Therefore, there will be 900 gallons of water left in the ship's tanks 60 days after leaving port.